Edge Universality of Beta Ensembles

Paul Bourgade; László Erdös; Horng Tzer Yau

doi:10.1007/s00220-014-2120-z

Edge Universality of Beta Ensembles

Paul Bourgade, László Erdös, Horng Tzer Yau

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the edge universality of the beta ensembles for any β ≥ 1, provided that the limiting spectrum is supported on a single interval, and the external potential is C⁴ and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class C⁴.

Original language	English (US)
Pages (from-to)	261-353
Number of pages	93
Journal	Communications In Mathematical Physics
Volume	332
Issue number	1
DOIs	https://doi.org/10.1007/s00220-014-2120-z
State	Published - Nov 2014

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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title = "Edge Universality of Beta Ensembles",

abstract = "We prove the edge universality of the beta ensembles for any β ≥ 1, provided that the limiting spectrum is supported on a single interval, and the external potential is C4 and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class C4.",

author = "Paul Bourgade and L{\'a}szl{\'o} Erd{\"o}s and Yau, {Horng Tzer}",

note = "Funding Information: L. Erd{\"o}s was partially supported by SFB-TR 12 Grant of the German Research Council. On leave from Institute of Mathematics, University of Munich, Germany. Funding Information: P. Bourgade was partially supported by NSF grant DMS-1208859. Funding Information: H.-T. Yau was partially supported by NSF grant DMS1307444 and Simons Investigator Award.",

year = "2014",

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doi = "10.1007/s00220-014-2120-z",

language = "English (US)",

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journal = "Communications In Mathematical Physics",

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AU - Bourgade, Paul

AU - Erdös, László

AU - Yau, Horng Tzer

N1 - Funding Information: L. Erdös was partially supported by SFB-TR 12 Grant of the German Research Council. On leave from Institute of Mathematics, University of Munich, Germany. Funding Information: P. Bourgade was partially supported by NSF grant DMS-1208859. Funding Information: H.-T. Yau was partially supported by NSF grant DMS1307444 and Simons Investigator Award.

PY - 2014/11

Y1 - 2014/11

N2 - We prove the edge universality of the beta ensembles for any β ≥ 1, provided that the limiting spectrum is supported on a single interval, and the external potential is C4 and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class C4.

AB - We prove the edge universality of the beta ensembles for any β ≥ 1, provided that the limiting spectrum is supported on a single interval, and the external potential is C4 and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class C4.

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Edge Universality of Beta Ensembles

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