Comparison Theory for Markov Chains on Different State Spaces and Application to Random Walk on Derangements
Abstract We consider two Markov chains on state spaces $$\Omega \subset \widehat{\Omega }$$. In this paper, we prove bounds on the eigenvalues of the chain on the smaller state space based on the eigenvalues of the chain on the larger state space. This generalizes work of Diaconis, Saloff-Coste, and...
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Gespeichert in:
| Autor*in: |
Smith, Aaron [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2014 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of theoretical probability - Springer US, 1988, 28(2014), 4 vom: 15. Mai, Seite 1406-1430 |
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| Übergeordnetes Werk: |
volume:28 ; year:2014 ; number:4 ; day:15 ; month:05 ; pages:1406-1430 |
| Links: |
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| DOI / URN: |
10.1007/s10959-014-0559-7 |
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OLC2053630272 |
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| 520 | |a Abstract We consider two Markov chains on state spaces $$\Omega \subset \widehat{\Omega }$$. In this paper, we prove bounds on the eigenvalues of the chain on the smaller state space based on the eigenvalues of the chain on the larger state space. This generalizes work of Diaconis, Saloff-Coste, and others on comparison of chains in the case $$\Omega = \widehat{\Omega }$$. The main tool is the extension of functions from the smaller space to the larger, which allows comparison of the entire spectrum of the two chains. The theory is used to give quick analyses of several chains without symmetry. We apply this theory to analyze the mixing properties of a ‘random transposition’ walk on derangements. | ||
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10.1007/s10959-014-0559-7 doi (DE-627)OLC2053630272 (DE-He213)s10959-014-0559-7-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Smith, Aaron verfasserin aut Comparison Theory for Markov Chains on Different State Spaces and Application to Random Walk on Derangements 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract We consider two Markov chains on state spaces $$\Omega \subset \widehat{\Omega }$$. In this paper, we prove bounds on the eigenvalues of the chain on the smaller state space based on the eigenvalues of the chain on the larger state space. This generalizes work of Diaconis, Saloff-Coste, and others on comparison of chains in the case $$\Omega = \widehat{\Omega }$$. The main tool is the extension of functions from the smaller space to the larger, which allows comparison of the entire spectrum of the two chains. The theory is used to give quick analyses of several chains without symmetry. We apply this theory to analyze the mixing properties of a ‘random transposition’ walk on derangements. Markov chain Mixing time Comparison Enthalten in Journal of theoretical probability Springer US, 1988 28(2014), 4 vom: 15. Mai, Seite 1406-1430 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:28 year:2014 number:4 day:15 month:05 pages:1406-1430 https://doi.org/10.1007/s10959-014-0559-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4325 AR 28 2014 4 15 05 1406-1430 |
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10.1007/s10959-014-0559-7 doi (DE-627)OLC2053630272 (DE-He213)s10959-014-0559-7-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Smith, Aaron verfasserin aut Comparison Theory for Markov Chains on Different State Spaces and Application to Random Walk on Derangements 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract We consider two Markov chains on state spaces $$\Omega \subset \widehat{\Omega }$$. In this paper, we prove bounds on the eigenvalues of the chain on the smaller state space based on the eigenvalues of the chain on the larger state space. This generalizes work of Diaconis, Saloff-Coste, and others on comparison of chains in the case $$\Omega = \widehat{\Omega }$$. The main tool is the extension of functions from the smaller space to the larger, which allows comparison of the entire spectrum of the two chains. The theory is used to give quick analyses of several chains without symmetry. We apply this theory to analyze the mixing properties of a ‘random transposition’ walk on derangements. Markov chain Mixing time Comparison Enthalten in Journal of theoretical probability Springer US, 1988 28(2014), 4 vom: 15. Mai, Seite 1406-1430 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:28 year:2014 number:4 day:15 month:05 pages:1406-1430 https://doi.org/10.1007/s10959-014-0559-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4325 AR 28 2014 4 15 05 1406-1430 |
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10.1007/s10959-014-0559-7 doi (DE-627)OLC2053630272 (DE-He213)s10959-014-0559-7-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Smith, Aaron verfasserin aut Comparison Theory for Markov Chains on Different State Spaces and Application to Random Walk on Derangements 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract We consider two Markov chains on state spaces $$\Omega \subset \widehat{\Omega }$$. In this paper, we prove bounds on the eigenvalues of the chain on the smaller state space based on the eigenvalues of the chain on the larger state space. This generalizes work of Diaconis, Saloff-Coste, and others on comparison of chains in the case $$\Omega = \widehat{\Omega }$$. The main tool is the extension of functions from the smaller space to the larger, which allows comparison of the entire spectrum of the two chains. The theory is used to give quick analyses of several chains without symmetry. We apply this theory to analyze the mixing properties of a ‘random transposition’ walk on derangements. Markov chain Mixing time Comparison Enthalten in Journal of theoretical probability Springer US, 1988 28(2014), 4 vom: 15. Mai, Seite 1406-1430 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:28 year:2014 number:4 day:15 month:05 pages:1406-1430 https://doi.org/10.1007/s10959-014-0559-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4325 AR 28 2014 4 15 05 1406-1430 |
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10.1007/s10959-014-0559-7 doi (DE-627)OLC2053630272 (DE-He213)s10959-014-0559-7-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Smith, Aaron verfasserin aut Comparison Theory for Markov Chains on Different State Spaces and Application to Random Walk on Derangements 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract We consider two Markov chains on state spaces $$\Omega \subset \widehat{\Omega }$$. In this paper, we prove bounds on the eigenvalues of the chain on the smaller state space based on the eigenvalues of the chain on the larger state space. This generalizes work of Diaconis, Saloff-Coste, and others on comparison of chains in the case $$\Omega = \widehat{\Omega }$$. The main tool is the extension of functions from the smaller space to the larger, which allows comparison of the entire spectrum of the two chains. The theory is used to give quick analyses of several chains without symmetry. We apply this theory to analyze the mixing properties of a ‘random transposition’ walk on derangements. Markov chain Mixing time Comparison Enthalten in Journal of theoretical probability Springer US, 1988 28(2014), 4 vom: 15. Mai, Seite 1406-1430 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:28 year:2014 number:4 day:15 month:05 pages:1406-1430 https://doi.org/10.1007/s10959-014-0559-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4325 AR 28 2014 4 15 05 1406-1430 |
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Abstract We consider two Markov chains on state spaces $$\Omega \subset \widehat{\Omega }$$. In this paper, we prove bounds on the eigenvalues of the chain on the smaller state space based on the eigenvalues of the chain on the larger state space. This generalizes work of Diaconis, Saloff-Coste, and others on comparison of chains in the case $$\Omega = \widehat{\Omega }$$. The main tool is the extension of functions from the smaller space to the larger, which allows comparison of the entire spectrum of the two chains. The theory is used to give quick analyses of several chains without symmetry. We apply this theory to analyze the mixing properties of a ‘random transposition’ walk on derangements. © Springer Science+Business Media New York 2014 |
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Abstract We consider two Markov chains on state spaces $$\Omega \subset \widehat{\Omega }$$. In this paper, we prove bounds on the eigenvalues of the chain on the smaller state space based on the eigenvalues of the chain on the larger state space. This generalizes work of Diaconis, Saloff-Coste, and others on comparison of chains in the case $$\Omega = \widehat{\Omega }$$. The main tool is the extension of functions from the smaller space to the larger, which allows comparison of the entire spectrum of the two chains. The theory is used to give quick analyses of several chains without symmetry. We apply this theory to analyze the mixing properties of a ‘random transposition’ walk on derangements. © Springer Science+Business Media New York 2014 |
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Abstract We consider two Markov chains on state spaces $$\Omega \subset \widehat{\Omega }$$. In this paper, we prove bounds on the eigenvalues of the chain on the smaller state space based on the eigenvalues of the chain on the larger state space. This generalizes work of Diaconis, Saloff-Coste, and others on comparison of chains in the case $$\Omega = \widehat{\Omega }$$. The main tool is the extension of functions from the smaller space to the larger, which allows comparison of the entire spectrum of the two chains. The theory is used to give quick analyses of several chains without symmetry. We apply this theory to analyze the mixing properties of a ‘random transposition’ walk on derangements. © Springer Science+Business Media New York 2014 |
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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">OLC2053630272</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503161034.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2014 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10959-014-0559-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2053630272</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10959-014-0559-7-p</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="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Smith, Aaron</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Comparison Theory for Markov Chains on Different State Spaces and Application to Random Walk on Derangements</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2014</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">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media New York 2014</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We consider two Markov chains on state spaces $$\Omega \subset \widehat{\Omega }$$. In this paper, we prove bounds on the eigenvalues of the chain on the smaller state space based on the eigenvalues of the chain on the larger state space. This generalizes work of Diaconis, Saloff-Coste, and others on comparison of chains in the case $$\Omega = \widehat{\Omega }$$. The main tool is the extension of functions from the smaller space to the larger, which allows comparison of the entire spectrum of the two chains. The theory is used to give quick analyses of several chains without symmetry. We apply this theory to analyze the mixing properties of a ‘random transposition’ walk on derangements.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Markov chain</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mixing time</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Comparison</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of theoretical probability</subfield><subfield code="d">Springer US, 1988</subfield><subfield code="g">28(2014), 4 vom: 15. Mai, Seite 1406-1430</subfield><subfield code="w">(DE-627)129930903</subfield><subfield code="w">(DE-600)357043-5</subfield><subfield code="w">(DE-576)018191886</subfield><subfield code="x">0894-9840</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:28</subfield><subfield code="g">year:2014</subfield><subfield code="g">number:4</subfield><subfield code="g">day:15</subfield><subfield code="g">month:05</subfield><subfield code="g">pages:1406-1430</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s10959-014-0559-7</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2002</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">28</subfield><subfield code="j">2014</subfield><subfield code="e">4</subfield><subfield code="b">15</subfield><subfield code="c">05</subfield><subfield code="h">1406-1430</subfield></datafield></record></collection>
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