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res:
bibo_abstract:
- 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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: László
foaf_name: László Erdös
foaf_surname: Erdös
foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0001-5366-9603
- foaf_Person:
foaf_givenName: Benjamin
foaf_name: Schlein, Benjamin
foaf_surname: Schlein
- foaf_Person:
foaf_givenName: Horng
foaf_name: Yau, Horng-Tzer
foaf_surname: Yau
bibo_doi: 10.1007/s00222-010-0302-7
bibo_issue: '1'
bibo_volume: 185
dct_date: 2011^xs_gYear
dct_publisher: Springer@
dct_title: Universality of random matrices and local relaxation flow@
...