10.1007/s00222-010-0302-7
László Erdös
László
Erdös0000-0001-5366-9603
Schlein, Benjamin
Benjamin
Schlein
Yau, Horng-Tzer
Horng
Yau
Universality of random matrices and local relaxation flow
Springer
2011
2018-12-11T11:59:29Z
2019-04-26T07:22:20Z
journal_article
https://research-explorer.app.ist.ac.at/record/2764
https://research-explorer.app.ist.ac.at/record/2764.json
Consider the Dyson Brownian motion with parameter β, where β=1,2,4 corresponds to the eigenvalue flows for the eigenvalues of symmetric, hermitian and quaternion self-dual ensembles. For any β≥1, we prove that the relaxation time to local equilibrium for the Dyson Brownian motion is bounded above by N -ζ for some ζ> 0. The proof is based on an estimate of the entropy flow of the Dyson Brownian motion w. r. t. a "pseudo equilibrium measure". As an application of this estimate, we prove that the eigenvalue spacing statistics in the bulk of the spectrum for N×N symmetric Wigner ensemble is the same as that of the Gaussian Orthogonal Ensemble (GOE) in the limit N→∞. The assumptions on the probability distribution of the matrix elements of the Wigner ensemble are a subexponential decay and some minor restriction on the support.