Continuum limits of random matrices and the Brownian carousel

Abstract We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general β siblings converge to Sine β, a translation invariant point process. This process has a geometric description in term of the Brownian carousel, a deterministic functio...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Valkó, Benedek [verfasserIn] Virág, Bálint

Format:	Artikel
Sprache:	Englisch

Erschienen:	2009

Schlagwörter:	Point Process Phase Function Random Matrice Continuum Limit Hyperbolic Plane

Systematik:	SA 5940 SA 5940

Anmerkung:	© Springer-Verlag 2009

Übergeordnetes Werk:	Enthalten in: Inventiones mathematicae - Springer-Verlag, 1966, 177(2009), 3 vom: 27. Feb., Seite 463-508
Übergeordnetes Werk:	volume:177 ; year:2009 ; number:3 ; day:27 ; month:02 ; pages:463-508

Links:	Volltext

DOI / URN:	10.1007/s00222-009-0180-z

Katalog-ID:	OLC2050922477

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allfields	10.1007/s00222-009-0180-z doi (DE-627)OLC2050922477 (DE-He213)s00222-009-0180-z-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn SA 5940 VZ rvk SA 5940 VZ rvk Valkó, Benedek verfasserin aut Continuum limits of random matrices and the Brownian carousel 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general β siblings converge to Sine β, a translation invariant point process. This process has a geometric description in term of the Brownian carousel, a deterministic function of Brownian motion in the hyperbolic plane. The Brownian carousel, a description of the a continuum limit of random matrices, provides a convenient way to analyze the limiting point processes. We show that the gap probability of Sine β is continuous in the gap size and β, and compute its asymptotics for large gaps. Moreover, the stochastic differential equation version of the Brownian carousel exhibits a phase transition at β=2. Point Process Phase Function Random Matrice Continuum Limit Hyperbolic Plane Virág, Bálint aut Enthalten in Inventiones mathematicae Springer-Verlag, 1966 177(2009), 3 vom: 27. Feb., Seite 463-508 (DE-627)129077453 (DE-600)2921-X (DE-576)014409992 0020-9910 nnns volume:177 year:2009 number:3 day:27 month:02 pages:463-508 https://doi.org/10.1007/s00222-009-0180-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 5940 SA 5940 AR 177 2009 3 27 02 463-508
spelling	10.1007/s00222-009-0180-z doi (DE-627)OLC2050922477 (DE-He213)s00222-009-0180-z-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn SA 5940 VZ rvk SA 5940 VZ rvk Valkó, Benedek verfasserin aut Continuum limits of random matrices and the Brownian carousel 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general β siblings converge to Sine β, a translation invariant point process. This process has a geometric description in term of the Brownian carousel, a deterministic function of Brownian motion in the hyperbolic plane. The Brownian carousel, a description of the a continuum limit of random matrices, provides a convenient way to analyze the limiting point processes. We show that the gap probability of Sine β is continuous in the gap size and β, and compute its asymptotics for large gaps. Moreover, the stochastic differential equation version of the Brownian carousel exhibits a phase transition at β=2. Point Process Phase Function Random Matrice Continuum Limit Hyperbolic Plane Virág, Bálint aut Enthalten in Inventiones mathematicae Springer-Verlag, 1966 177(2009), 3 vom: 27. Feb., Seite 463-508 (DE-627)129077453 (DE-600)2921-X (DE-576)014409992 0020-9910 nnns volume:177 year:2009 number:3 day:27 month:02 pages:463-508 https://doi.org/10.1007/s00222-009-0180-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 5940 SA 5940 AR 177 2009 3 27 02 463-508
allfields_unstemmed	10.1007/s00222-009-0180-z doi (DE-627)OLC2050922477 (DE-He213)s00222-009-0180-z-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn SA 5940 VZ rvk SA 5940 VZ rvk Valkó, Benedek verfasserin aut Continuum limits of random matrices and the Brownian carousel 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general β siblings converge to Sine β, a translation invariant point process. This process has a geometric description in term of the Brownian carousel, a deterministic function of Brownian motion in the hyperbolic plane. The Brownian carousel, a description of the a continuum limit of random matrices, provides a convenient way to analyze the limiting point processes. We show that the gap probability of Sine β is continuous in the gap size and β, and compute its asymptotics for large gaps. Moreover, the stochastic differential equation version of the Brownian carousel exhibits a phase transition at β=2. Point Process Phase Function Random Matrice Continuum Limit Hyperbolic Plane Virág, Bálint aut Enthalten in Inventiones mathematicae Springer-Verlag, 1966 177(2009), 3 vom: 27. Feb., Seite 463-508 (DE-627)129077453 (DE-600)2921-X (DE-576)014409992 0020-9910 nnns volume:177 year:2009 number:3 day:27 month:02 pages:463-508 https://doi.org/10.1007/s00222-009-0180-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 5940 SA 5940 AR 177 2009 3 27 02 463-508
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allfieldsSound	10.1007/s00222-009-0180-z doi (DE-627)OLC2050922477 (DE-He213)s00222-009-0180-z-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn SA 5940 VZ rvk SA 5940 VZ rvk Valkó, Benedek verfasserin aut Continuum limits of random matrices and the Brownian carousel 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general β siblings converge to Sine β, a translation invariant point process. This process has a geometric description in term of the Brownian carousel, a deterministic function of Brownian motion in the hyperbolic plane. The Brownian carousel, a description of the a continuum limit of random matrices, provides a convenient way to analyze the limiting point processes. We show that the gap probability of Sine β is continuous in the gap size and β, and compute its asymptotics for large gaps. Moreover, the stochastic differential equation version of the Brownian carousel exhibits a phase transition at β=2. Point Process Phase Function Random Matrice Continuum Limit Hyperbolic Plane Virág, Bálint aut Enthalten in Inventiones mathematicae Springer-Verlag, 1966 177(2009), 3 vom: 27. Feb., Seite 463-508 (DE-627)129077453 (DE-600)2921-X (DE-576)014409992 0020-9910 nnns volume:177 year:2009 number:3 day:27 month:02 pages:463-508 https://doi.org/10.1007/s00222-009-0180-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 5940 SA 5940 AR 177 2009 3 27 02 463-508
language	English
source	Enthalten in Inventiones mathematicae 177(2009), 3 vom: 27. Feb., Seite 463-508 volume:177 year:2009 number:3 day:27 month:02 pages:463-508
sourceStr	Enthalten in Inventiones mathematicae 177(2009), 3 vom: 27. Feb., Seite 463-508 volume:177 year:2009 number:3 day:27 month:02 pages:463-508
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author	Valkó, Benedek
spellingShingle	Valkó, Benedek ddc 510 ssgn 17,1 rvk SA 5940 misc Point Process misc Phase Function misc Random Matrice misc Continuum Limit misc Hyperbolic Plane Continuum limits of random matrices and the Brownian carousel
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topic_title	510 VZ 17,1 ssgn SA 5940 VZ rvk Continuum limits of random matrices and the Brownian carousel Point Process Phase Function Random Matrice Continuum Limit Hyperbolic Plane
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title	Continuum limits of random matrices and the Brownian carousel
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title_full	Continuum limits of random matrices and the Brownian carousel
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author_browse	Valkó, Benedek Virág, Bálint
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title_sort	continuum limits of random matrices and the brownian carousel
title_auth	Continuum limits of random matrices and the Brownian carousel
abstract	Abstract We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general β siblings converge to Sine β, a translation invariant point process. This process has a geometric description in term of the Brownian carousel, a deterministic function of Brownian motion in the hyperbolic plane. The Brownian carousel, a description of the a continuum limit of random matrices, provides a convenient way to analyze the limiting point processes. We show that the gap probability of Sine β is continuous in the gap size and β, and compute its asymptotics for large gaps. Moreover, the stochastic differential equation version of the Brownian carousel exhibits a phase transition at β=2. © Springer-Verlag 2009
abstractGer	Abstract We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general β siblings converge to Sine β, a translation invariant point process. This process has a geometric description in term of the Brownian carousel, a deterministic function of Brownian motion in the hyperbolic plane. The Brownian carousel, a description of the a continuum limit of random matrices, provides a convenient way to analyze the limiting point processes. We show that the gap probability of Sine β is continuous in the gap size and β, and compute its asymptotics for large gaps. Moreover, the stochastic differential equation version of the Brownian carousel exhibits a phase transition at β=2. © Springer-Verlag 2009
abstract_unstemmed	Abstract We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general β siblings converge to Sine β, a translation invariant point process. This process has a geometric description in term of the Brownian carousel, a deterministic function of Brownian motion in the hyperbolic plane. The Brownian carousel, a description of the a continuum limit of random matrices, provides a convenient way to analyze the limiting point processes. We show that the gap probability of Sine β is continuous in the gap size and β, and compute its asymptotics for large gaps. Moreover, the stochastic differential equation version of the Brownian carousel exhibits a phase transition at β=2. © Springer-Verlag 2009
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title_short	Continuum limits of random matrices and the Brownian carousel
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