Tracy-Widom GUE law and symplectic invariants

We establish the relation between two objects: an integrable system related to Painleve II equation, and the symplectic invariants of a certain plane curve \Sigma_{TW} describing the average eigenvalue density of a random hermitian matrix spectrum near a hard edge (a bound for its maximal eigenvalue...

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Detalles Bibliográficos
Autores principales: Borot, Gaetan, Eynard, Bertrand
Lenguaje:eng
Publicado: 2010
Materias:
Nonlinear Systems
Acceso en línea:http://cds.cern.ch/record/1305323
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author Borot, Gaetan
Eynard, Bertrand
author_facet Borot, Gaetan
Eynard, Bertrand
author_sort Borot, Gaetan
collection CERN
description We establish the relation between two objects: an integrable system related to Painleve II equation, and the symplectic invariants of a certain plane curve \Sigma_{TW} describing the average eigenvalue density of a random hermitian matrix spectrum near a hard edge (a bound for its maximal eigenvalue). This explains directly how the Tracy-Widow law F_{GUE}, governing the distribution of the maximal eigenvalue in hermitian random matrices, can also be recovered from symplectic invariants.
id cern-1305323
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2010
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spelling cern-13053232019-10-04T11:32:54Zhttp://cds.cern.ch/record/1305323engBorot, GaetanEynard, BertrandTracy-Widom GUE law and symplectic invariantsNonlinear SystemsWe establish the relation between two objects: an integrable system related to Painleve II equation, and the symplectic invariants of a certain plane curve \Sigma_{TW} describing the average eigenvalue density of a random hermitian matrix spectrum near a hard edge (a bound for its maximal eigenvalue). This explains directly how the Tracy-Widow law F_{GUE}, governing the distribution of the maximal eigenvalue in hermitian random matrices, can also be recovered from symplectic invariants.arXiv:1011.1418CERN-PH-TH-2010-265IPhT-T10-166oai:cds.cern.ch:13053232010-11-08
spellingShingle Nonlinear Systems
Borot, Gaetan
Eynard, Bertrand
Tracy-Widom GUE law and symplectic invariants
title Tracy-Widom GUE law and symplectic invariants
title_full Tracy-Widom GUE law and symplectic invariants
title_fullStr Tracy-Widom GUE law and symplectic invariants
title_full_unstemmed Tracy-Widom GUE law and symplectic invariants
title_short Tracy-Widom GUE law and symplectic invariants
title_sort tracy-widom gue law and symplectic invariants
topic Nonlinear Systems
url http://cds.cern.ch/record/1305323
work_keys_str_mv AT borotgaetan tracywidomguelawandsymplecticinvariants
AT eynardbertrand tracywidomguelawandsymplecticinvariants

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