Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 3, pp. 335-365
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L. Pastur; M. Shcherbina. On the edge universality of the local eigenvalue statistics of matrix models. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 3, pp. 335-365. http://geodesic.mathdoc.fr/item/JMAG_2003_10_3_a5/
@article{JMAG_2003_10_3_a5,
author = {L. Pastur and M. Shcherbina},
title = {On the edge universality of the local eigenvalue statistics of matrix models},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {335--365},
year = {2003},
volume = {10},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_2003_10_3_a5/}
}
TY - JOUR
AU - L. Pastur
AU - M. Shcherbina
TI - On the edge universality of the local eigenvalue statistics of matrix models
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 2003
SP - 335
EP - 365
VL - 10
IS - 3
UR - http://geodesic.mathdoc.fr/item/JMAG_2003_10_3_a5/
LA - en
ID - JMAG_2003_10_3_a5
ER -
%0 Journal Article
%A L. Pastur
%A M. Shcherbina
%T On the edge universality of the local eigenvalue statistics of matrix models
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2003
%P 335-365
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_2003_10_3_a5/
%G en
%F JMAG_2003_10_3_a5
Basing on our recent results on the $1/n$-expansion in unitary invariant random matrix ensembles, known as matrix models, we prove that the local eigenvalue statistic, arising in a certain neighborhood of the edges of the support of the density of states, is independent of the form of the potential, determining the matrix model. Our proof is applicable to the case of real analytic potentials and of supports, consisting of one or two disjoint intervals.
