On Universality for Orthogonal Ensembles of Random Matrices
Abstract We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the pro...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Shcherbina, M. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2008 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2008 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer-Verlag, 1965, 285(2008), 3 vom: 23. Okt., Seite 957-974 |
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| Übergeordnetes Werk: |
volume:285 ; year:2008 ; number:3 ; day:23 ; month:10 ; pages:957-974 |
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| DOI / URN: |
10.1007/s00220-008-0648-5 |
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10.1007/s00220-008-0648-5 doi (DE-627)OLC2038894906 (DE-He213)s00220-008-0648-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Shcherbina, M. verfasserin aut On Universality for Orthogonal Ensembles of Random Matrices 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a product of a positive Toeplitz matrix and a two diagonal skew symmetric Toeplitz matrix. Matrix Model Orthogonal Polynomial Random Matrice Random Matrix Random Matrix Theory Enthalten in Communications in mathematical physics Springer-Verlag, 1965 285(2008), 3 vom: 23. Okt., Seite 957-974 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:285 year:2008 number:3 day:23 month:10 pages:957-974 https://doi.org/10.1007/s00220-008-0648-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 285 2008 3 23 10 957-974 |
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10.1007/s00220-008-0648-5 doi (DE-627)OLC2038894906 (DE-He213)s00220-008-0648-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Shcherbina, M. verfasserin aut On Universality for Orthogonal Ensembles of Random Matrices 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a product of a positive Toeplitz matrix and a two diagonal skew symmetric Toeplitz matrix. Matrix Model Orthogonal Polynomial Random Matrice Random Matrix Random Matrix Theory Enthalten in Communications in mathematical physics Springer-Verlag, 1965 285(2008), 3 vom: 23. Okt., Seite 957-974 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:285 year:2008 number:3 day:23 month:10 pages:957-974 https://doi.org/10.1007/s00220-008-0648-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 285 2008 3 23 10 957-974 |
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10.1007/s00220-008-0648-5 doi (DE-627)OLC2038894906 (DE-He213)s00220-008-0648-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Shcherbina, M. verfasserin aut On Universality for Orthogonal Ensembles of Random Matrices 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a product of a positive Toeplitz matrix and a two diagonal skew symmetric Toeplitz matrix. Matrix Model Orthogonal Polynomial Random Matrice Random Matrix Random Matrix Theory Enthalten in Communications in mathematical physics Springer-Verlag, 1965 285(2008), 3 vom: 23. Okt., Seite 957-974 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:285 year:2008 number:3 day:23 month:10 pages:957-974 https://doi.org/10.1007/s00220-008-0648-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 285 2008 3 23 10 957-974 |
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10.1007/s00220-008-0648-5 doi (DE-627)OLC2038894906 (DE-He213)s00220-008-0648-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Shcherbina, M. verfasserin aut On Universality for Orthogonal Ensembles of Random Matrices 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a product of a positive Toeplitz matrix and a two diagonal skew symmetric Toeplitz matrix. Matrix Model Orthogonal Polynomial Random Matrice Random Matrix Random Matrix Theory Enthalten in Communications in mathematical physics Springer-Verlag, 1965 285(2008), 3 vom: 23. Okt., Seite 957-974 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:285 year:2008 number:3 day:23 month:10 pages:957-974 https://doi.org/10.1007/s00220-008-0648-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 285 2008 3 23 10 957-974 |
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10.1007/s00220-008-0648-5 doi (DE-627)OLC2038894906 (DE-He213)s00220-008-0648-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Shcherbina, M. verfasserin aut On Universality for Orthogonal Ensembles of Random Matrices 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a product of a positive Toeplitz matrix and a two diagonal skew symmetric Toeplitz matrix. Matrix Model Orthogonal Polynomial Random Matrice Random Matrix Random Matrix Theory Enthalten in Communications in mathematical physics Springer-Verlag, 1965 285(2008), 3 vom: 23. Okt., Seite 957-974 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:285 year:2008 number:3 day:23 month:10 pages:957-974 https://doi.org/10.1007/s00220-008-0648-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 285 2008 3 23 10 957-974 |
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Abstract We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a product of a positive Toeplitz matrix and a two diagonal skew symmetric Toeplitz matrix. © Springer-Verlag 2008 |
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Abstract We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a product of a positive Toeplitz matrix and a two diagonal skew symmetric Toeplitz matrix. © Springer-Verlag 2008 |
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Abstract We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a product of a positive Toeplitz matrix and a two diagonal skew symmetric Toeplitz matrix. © Springer-Verlag 2008 |
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On Universality for Orthogonal Ensembles of Random Matrices |
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