Edge Universality of Beta Ensembles

2013/06/30 by Paul Bourgade, László Erdős, Laszlo Erdos +2
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #BETA (programming language) #Combinatorics #Computer science #Limiting #Mathematical physics #Mathematics #Physics #Quantum mechanics #Random Matrices and Applications #Renormalization group #Statistical physics #Universality (dynamical systems) #math-ph #math.MP #math.PR #msc:15B52 #msc:82B44

paper · pdf · doi:10.1007/s00220-014-2120-z

87 pages

arxiv created 2014/05/17 · openalex publication_date 2014/08/20 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 \mathscrC⁴ 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 \mathscrC⁴.

Citations

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