Singular Values for Products of Complex Ginibre Matrices with a Source: Hard Edge Limit and Phase Transition
Abstract The singular values squared of the random matrix product %${Y = {G_{r} G_{r-1}} \ldots G_{1} (G_{0} + A)}%$, where each %${G_{j}}%$ is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a d...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Forrester, Peter J. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Berlin : Springer, 1965, 344(2015), 1 vom: 30. Nov., Seite 333-368 |
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| Übergeordnetes Werk: |
volume:344 ; year:2015 ; number:1 ; day:30 ; month:11 ; pages:333-368 |
| Links: |
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| DOI / URN: |
10.1007/s00220-015-2507-5 |
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SPR002363011 |
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| 100 | 1 | |a Forrester, Peter J. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Singular Values for Products of Complex Ginibre Matrices with a Source: Hard Edge Limit and Phase Transition |
| 264 | 1 | |c 2015 | |
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| 520 | |a Abstract The singular values squared of the random matrix product %${Y = {G_{r} G_{r-1}} \ldots G_{1} (G_{0} + A)}%$, where each %${G_{j}}%$ is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a double contour integral. When all but finitely many eigenvalues of A*A are equal to bN, the kernel is shown to admit a well-defined hard edge scaling, in which case a critical value is established and a phase transition phenomenon is observed. More specifically, the limiting kernel in the subcritical regime of %${0 < b < 1}%$ is independent of b, and is in fact the same as that known for the case b = 0 due to Kuijlaars and Zhang. The critical regime of b = 1 allows for a double scaling limit by choosing %${{b = (1 - \tau/\sqrt{N})^{-1}}}%$, and for this the critical kernel and outlier phenomenon are established. In the simplest case r = 0, which is closely related to non-intersecting squared Bessel paths, a distribution corresponding to the finite shifted mean LUE is proven to be the scaling limit in the supercritical regime of %${b > 1}%$ with two distinct scaling rates. Similar results also hold true for the random matrix product %${T_{r} T_{r-1} \ldots T_{1} (G_{0} + A)}%$, with each %${T_{j}}%$ being a truncated unitary matrix. | ||
| 650 | 4 | |a Random Matrice |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Random Matrix |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Random Matrix Theory |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Eigenvalue Density |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Global Density |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Liu, Dang-Zheng |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Communications in mathematical physics |d Berlin : Springer, 1965 |g 344(2015), 1 vom: 30. Nov., Seite 333-368 |w (DE-627)253721628 |w (DE-600)1458931-X |x 1432-0916 |7 nnns |
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10.1007/s00220-015-2507-5 doi (DE-627)SPR002363011 (SPR)s00220-015-2507-5-e DE-627 ger DE-627 rakwb eng Forrester, Peter J. verfasserin aut Singular Values for Products of Complex Ginibre Matrices with a Source: Hard Edge Limit and Phase Transition 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract The singular values squared of the random matrix product %${Y = {G_{r} G_{r-1}} \ldots G_{1} (G_{0} + A)}%$, where each %${G_{j}}%$ is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a double contour integral. When all but finitely many eigenvalues of A*A are equal to bN, the kernel is shown to admit a well-defined hard edge scaling, in which case a critical value is established and a phase transition phenomenon is observed. More specifically, the limiting kernel in the subcritical regime of %${0 < b < 1}%$ is independent of b, and is in fact the same as that known for the case b = 0 due to Kuijlaars and Zhang. The critical regime of b = 1 allows for a double scaling limit by choosing %${{b = (1 - \tau/\sqrt{N})^{-1}}}%$, and for this the critical kernel and outlier phenomenon are established. In the simplest case r = 0, which is closely related to non-intersecting squared Bessel paths, a distribution corresponding to the finite shifted mean LUE is proven to be the scaling limit in the supercritical regime of %${b > 1}%$ with two distinct scaling rates. Similar results also hold true for the random matrix product %${T_{r} T_{r-1} \ldots T_{1} (G_{0} + A)}%$, with each %${T_{j}}%$ being a truncated unitary matrix. Random Matrice (dpeaa)DE-He213 Random Matrix (dpeaa)DE-He213 Random Matrix Theory (dpeaa)DE-He213 Eigenvalue Density (dpeaa)DE-He213 Global Density (dpeaa)DE-He213 Liu, Dang-Zheng aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 344(2015), 1 vom: 30. Nov., Seite 333-368 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:344 year:2015 number:1 day:30 month:11 pages:333-368 https://dx.doi.org/10.1007/s00220-015-2507-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 344 2015 1 30 11 333-368 |
| spelling |
10.1007/s00220-015-2507-5 doi (DE-627)SPR002363011 (SPR)s00220-015-2507-5-e DE-627 ger DE-627 rakwb eng Forrester, Peter J. verfasserin aut Singular Values for Products of Complex Ginibre Matrices with a Source: Hard Edge Limit and Phase Transition 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract The singular values squared of the random matrix product %${Y = {G_{r} G_{r-1}} \ldots G_{1} (G_{0} + A)}%$, where each %${G_{j}}%$ is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a double contour integral. When all but finitely many eigenvalues of A*A are equal to bN, the kernel is shown to admit a well-defined hard edge scaling, in which case a critical value is established and a phase transition phenomenon is observed. More specifically, the limiting kernel in the subcritical regime of %${0 < b < 1}%$ is independent of b, and is in fact the same as that known for the case b = 0 due to Kuijlaars and Zhang. The critical regime of b = 1 allows for a double scaling limit by choosing %${{b = (1 - \tau/\sqrt{N})^{-1}}}%$, and for this the critical kernel and outlier phenomenon are established. In the simplest case r = 0, which is closely related to non-intersecting squared Bessel paths, a distribution corresponding to the finite shifted mean LUE is proven to be the scaling limit in the supercritical regime of %${b > 1}%$ with two distinct scaling rates. Similar results also hold true for the random matrix product %${T_{r} T_{r-1} \ldots T_{1} (G_{0} + A)}%$, with each %${T_{j}}%$ being a truncated unitary matrix. Random Matrice (dpeaa)DE-He213 Random Matrix (dpeaa)DE-He213 Random Matrix Theory (dpeaa)DE-He213 Eigenvalue Density (dpeaa)DE-He213 Global Density (dpeaa)DE-He213 Liu, Dang-Zheng aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 344(2015), 1 vom: 30. Nov., Seite 333-368 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:344 year:2015 number:1 day:30 month:11 pages:333-368 https://dx.doi.org/10.1007/s00220-015-2507-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 344 2015 1 30 11 333-368 |
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10.1007/s00220-015-2507-5 doi (DE-627)SPR002363011 (SPR)s00220-015-2507-5-e DE-627 ger DE-627 rakwb eng Forrester, Peter J. verfasserin aut Singular Values for Products of Complex Ginibre Matrices with a Source: Hard Edge Limit and Phase Transition 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract The singular values squared of the random matrix product %${Y = {G_{r} G_{r-1}} \ldots G_{1} (G_{0} + A)}%$, where each %${G_{j}}%$ is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a double contour integral. When all but finitely many eigenvalues of A*A are equal to bN, the kernel is shown to admit a well-defined hard edge scaling, in which case a critical value is established and a phase transition phenomenon is observed. More specifically, the limiting kernel in the subcritical regime of %${0 < b < 1}%$ is independent of b, and is in fact the same as that known for the case b = 0 due to Kuijlaars and Zhang. The critical regime of b = 1 allows for a double scaling limit by choosing %${{b = (1 - \tau/\sqrt{N})^{-1}}}%$, and for this the critical kernel and outlier phenomenon are established. In the simplest case r = 0, which is closely related to non-intersecting squared Bessel paths, a distribution corresponding to the finite shifted mean LUE is proven to be the scaling limit in the supercritical regime of %${b > 1}%$ with two distinct scaling rates. Similar results also hold true for the random matrix product %${T_{r} T_{r-1} \ldots T_{1} (G_{0} + A)}%$, with each %${T_{j}}%$ being a truncated unitary matrix. Random Matrice (dpeaa)DE-He213 Random Matrix (dpeaa)DE-He213 Random Matrix Theory (dpeaa)DE-He213 Eigenvalue Density (dpeaa)DE-He213 Global Density (dpeaa)DE-He213 Liu, Dang-Zheng aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 344(2015), 1 vom: 30. Nov., Seite 333-368 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:344 year:2015 number:1 day:30 month:11 pages:333-368 https://dx.doi.org/10.1007/s00220-015-2507-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 344 2015 1 30 11 333-368 |
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10.1007/s00220-015-2507-5 doi (DE-627)SPR002363011 (SPR)s00220-015-2507-5-e DE-627 ger DE-627 rakwb eng Forrester, Peter J. verfasserin aut Singular Values for Products of Complex Ginibre Matrices with a Source: Hard Edge Limit and Phase Transition 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract The singular values squared of the random matrix product %${Y = {G_{r} G_{r-1}} \ldots G_{1} (G_{0} + A)}%$, where each %${G_{j}}%$ is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a double contour integral. When all but finitely many eigenvalues of A*A are equal to bN, the kernel is shown to admit a well-defined hard edge scaling, in which case a critical value is established and a phase transition phenomenon is observed. More specifically, the limiting kernel in the subcritical regime of %${0 < b < 1}%$ is independent of b, and is in fact the same as that known for the case b = 0 due to Kuijlaars and Zhang. The critical regime of b = 1 allows for a double scaling limit by choosing %${{b = (1 - \tau/\sqrt{N})^{-1}}}%$, and for this the critical kernel and outlier phenomenon are established. In the simplest case r = 0, which is closely related to non-intersecting squared Bessel paths, a distribution corresponding to the finite shifted mean LUE is proven to be the scaling limit in the supercritical regime of %${b > 1}%$ with two distinct scaling rates. Similar results also hold true for the random matrix product %${T_{r} T_{r-1} \ldots T_{1} (G_{0} + A)}%$, with each %${T_{j}}%$ being a truncated unitary matrix. Random Matrice (dpeaa)DE-He213 Random Matrix (dpeaa)DE-He213 Random Matrix Theory (dpeaa)DE-He213 Eigenvalue Density (dpeaa)DE-He213 Global Density (dpeaa)DE-He213 Liu, Dang-Zheng aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 344(2015), 1 vom: 30. Nov., Seite 333-368 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:344 year:2015 number:1 day:30 month:11 pages:333-368 https://dx.doi.org/10.1007/s00220-015-2507-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 344 2015 1 30 11 333-368 |
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10.1007/s00220-015-2507-5 doi (DE-627)SPR002363011 (SPR)s00220-015-2507-5-e DE-627 ger DE-627 rakwb eng Forrester, Peter J. verfasserin aut Singular Values for Products of Complex Ginibre Matrices with a Source: Hard Edge Limit and Phase Transition 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract The singular values squared of the random matrix product %${Y = {G_{r} G_{r-1}} \ldots G_{1} (G_{0} + A)}%$, where each %${G_{j}}%$ is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a double contour integral. When all but finitely many eigenvalues of A*A are equal to bN, the kernel is shown to admit a well-defined hard edge scaling, in which case a critical value is established and a phase transition phenomenon is observed. More specifically, the limiting kernel in the subcritical regime of %${0 < b < 1}%$ is independent of b, and is in fact the same as that known for the case b = 0 due to Kuijlaars and Zhang. The critical regime of b = 1 allows for a double scaling limit by choosing %${{b = (1 - \tau/\sqrt{N})^{-1}}}%$, and for this the critical kernel and outlier phenomenon are established. In the simplest case r = 0, which is closely related to non-intersecting squared Bessel paths, a distribution corresponding to the finite shifted mean LUE is proven to be the scaling limit in the supercritical regime of %${b > 1}%$ with two distinct scaling rates. Similar results also hold true for the random matrix product %${T_{r} T_{r-1} \ldots T_{1} (G_{0} + A)}%$, with each %${T_{j}}%$ being a truncated unitary matrix. Random Matrice (dpeaa)DE-He213 Random Matrix (dpeaa)DE-He213 Random Matrix Theory (dpeaa)DE-He213 Eigenvalue Density (dpeaa)DE-He213 Global Density (dpeaa)DE-He213 Liu, Dang-Zheng aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 344(2015), 1 vom: 30. Nov., Seite 333-368 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:344 year:2015 number:1 day:30 month:11 pages:333-368 https://dx.doi.org/10.1007/s00220-015-2507-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 344 2015 1 30 11 333-368 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR002363011</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327161802.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2015 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00220-015-2507-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR002363011</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00220-015-2507-5-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Forrester, Peter J.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Singular Values for Products of Complex Ginibre Matrices with a Source: Hard Edge Limit and Phase Transition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag Berlin Heidelberg 2015</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The singular values squared of the random matrix product %${Y = {G_{r} G_{r-1}} \ldots G_{1} (G_{0} + A)}%$, where each %${G_{j}}%$ is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a double contour integral. When all but finitely many eigenvalues of A*A are equal to bN, the kernel is shown to admit a well-defined hard edge scaling, in which case a critical value is established and a phase transition phenomenon is observed. More specifically, the limiting kernel in the subcritical regime of %${0 < b < 1}%$ is independent of b, and is in fact the same as that known for the case b = 0 due to Kuijlaars and Zhang. The critical regime of b = 1 allows for a double scaling limit by choosing %${{b = (1 - \tau/\sqrt{N})^{-1}}}%$, and for this the critical kernel and outlier phenomenon are established. In the simplest case r = 0, which is closely related to non-intersecting squared Bessel paths, a distribution corresponding to the finite shifted mean LUE is proven to be the scaling limit in the supercritical regime of %${b > 1}%$ with two distinct scaling rates. Similar results also hold true for the random matrix product %${T_{r} T_{r-1} \ldots T_{1} (G_{0} + A)}%$, with each %${T_{j}}%$ being a truncated unitary matrix.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random Matrice</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random Matrix</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random Matrix Theory</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Eigenvalue Density</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global Density</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Liu, Dang-Zheng</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Communications in mathematical physics</subfield><subfield code="d">Berlin : Springer, 1965</subfield><subfield code="g">344(2015), 1 vom: 30. 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Singular Values for Products of Complex Ginibre Matrices with a Source: Hard Edge Limit and Phase Transition Random Matrice (dpeaa)DE-He213 Random Matrix (dpeaa)DE-He213 Random Matrix Theory (dpeaa)DE-He213 Eigenvalue Density (dpeaa)DE-He213 Global Density (dpeaa)DE-He213 |
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singular values for products of complex ginibre matrices with a source: hard edge limit and phase transition |
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Singular Values for Products of Complex Ginibre Matrices with a Source: Hard Edge Limit and Phase Transition |
| abstract |
Abstract The singular values squared of the random matrix product %${Y = {G_{r} G_{r-1}} \ldots G_{1} (G_{0} + A)}%$, where each %${G_{j}}%$ is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a double contour integral. When all but finitely many eigenvalues of A*A are equal to bN, the kernel is shown to admit a well-defined hard edge scaling, in which case a critical value is established and a phase transition phenomenon is observed. More specifically, the limiting kernel in the subcritical regime of %${0 < b < 1}%$ is independent of b, and is in fact the same as that known for the case b = 0 due to Kuijlaars and Zhang. The critical regime of b = 1 allows for a double scaling limit by choosing %${{b = (1 - \tau/\sqrt{N})^{-1}}}%$, and for this the critical kernel and outlier phenomenon are established. In the simplest case r = 0, which is closely related to non-intersecting squared Bessel paths, a distribution corresponding to the finite shifted mean LUE is proven to be the scaling limit in the supercritical regime of %${b > 1}%$ with two distinct scaling rates. Similar results also hold true for the random matrix product %${T_{r} T_{r-1} \ldots T_{1} (G_{0} + A)}%$, with each %${T_{j}}%$ being a truncated unitary matrix. © Springer-Verlag Berlin Heidelberg 2015 |
| abstractGer |
Abstract The singular values squared of the random matrix product %${Y = {G_{r} G_{r-1}} \ldots G_{1} (G_{0} + A)}%$, where each %${G_{j}}%$ is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a double contour integral. When all but finitely many eigenvalues of A*A are equal to bN, the kernel is shown to admit a well-defined hard edge scaling, in which case a critical value is established and a phase transition phenomenon is observed. More specifically, the limiting kernel in the subcritical regime of %${0 < b < 1}%$ is independent of b, and is in fact the same as that known for the case b = 0 due to Kuijlaars and Zhang. The critical regime of b = 1 allows for a double scaling limit by choosing %${{b = (1 - \tau/\sqrt{N})^{-1}}}%$, and for this the critical kernel and outlier phenomenon are established. In the simplest case r = 0, which is closely related to non-intersecting squared Bessel paths, a distribution corresponding to the finite shifted mean LUE is proven to be the scaling limit in the supercritical regime of %${b > 1}%$ with two distinct scaling rates. Similar results also hold true for the random matrix product %${T_{r} T_{r-1} \ldots T_{1} (G_{0} + A)}%$, with each %${T_{j}}%$ being a truncated unitary matrix. © Springer-Verlag Berlin Heidelberg 2015 |
| abstract_unstemmed |
Abstract The singular values squared of the random matrix product %${Y = {G_{r} G_{r-1}} \ldots G_{1} (G_{0} + A)}%$, where each %${G_{j}}%$ is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a double contour integral. When all but finitely many eigenvalues of A*A are equal to bN, the kernel is shown to admit a well-defined hard edge scaling, in which case a critical value is established and a phase transition phenomenon is observed. More specifically, the limiting kernel in the subcritical regime of %${0 < b < 1}%$ is independent of b, and is in fact the same as that known for the case b = 0 due to Kuijlaars and Zhang. The critical regime of b = 1 allows for a double scaling limit by choosing %${{b = (1 - \tau/\sqrt{N})^{-1}}}%$, and for this the critical kernel and outlier phenomenon are established. In the simplest case r = 0, which is closely related to non-intersecting squared Bessel paths, a distribution corresponding to the finite shifted mean LUE is proven to be the scaling limit in the supercritical regime of %${b > 1}%$ with two distinct scaling rates. Similar results also hold true for the random matrix product %${T_{r} T_{r-1} \ldots T_{1} (G_{0} + A)}%$, with each %${T_{j}}%$ being a truncated unitary matrix. © Springer-Verlag Berlin Heidelberg 2015 |
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| title_short |
Singular Values for Products of Complex Ginibre Matrices with a Source: Hard Edge Limit and Phase Transition |
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https://dx.doi.org/10.1007/s00220-015-2507-5 |
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Liu, Dang-Zheng |
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10.1007/s00220-015-2507-5 |
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| score |
7.3984165 |