Edge Universality of Beta Ensembles

Paul Bourgade, László Erdös, Horng Tzer Yau

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)261-353
Number of pages93
JournalCommunications in Mathematical Physics
Volume332
Issue number1
DOIs
StatePublished - 2014

Fingerprint

Universality
Ensemble
Limiting
intervals
Symmetry
Interval
symmetry
matrices
Class

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Edge Universality of Beta Ensembles. / Bourgade, Paul; Erdös, László; Yau, Horng Tzer.

In: Communications in Mathematical Physics, Vol. 332, No. 1, 2014, p. 261-353.

Research output: Contribution to journalArticle

Bourgade, Paul ; Erdös, László ; Yau, Horng Tzer. / Edge Universality of Beta Ensembles. In: Communications in Mathematical Physics. 2014 ; Vol. 332, No. 1. pp. 261-353.
@article{2eeb2f91487c4e22a82327b9e40bf53c,
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}",
year = "2014",
doi = "10.1007/s00220-014-2120-z",
language = "English (US)",
volume = "332",
pages = "261--353",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "1",

}

TY - JOUR

T1 - Edge Universality of Beta Ensembles

AU - Bourgade, Paul

AU - Erdös, László

AU - Yau, Horng Tzer

PY - 2014

Y1 - 2014

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.

UR - http://www.scopus.com/inward/record.url?scp=84906908735&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84906908735&partnerID=8YFLogxK

U2 - 10.1007/s00220-014-2120-z

DO - 10.1007/s00220-014-2120-z

M3 - Article

VL - 332

SP - 261

EP - 353

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -