---
res:
bibo_abstract:
- In this paper, we consider the ensemble of n×n Wigner Hermitian matrices H = (hℓk)1≤ℓ,k≤n
that generalize the Gaussian unitary ensemble (GUE). The matrix elements hℓk =
h̄ℓk are given by hℓk = n ?1/2(xℓk + √?1yℓk), where xℓk, yℓk for 1 ≤ ℓ < k
≤ n are i.i.d. random variables with mean zero and variance 1/2, yℓ ℓ = 0 and
xℓ ℓ have mean zero and variance 1. We assume the distribution of xℓk, yℓk to
have subexponential decay. In [3], four of the authors recently established that
the gap distribution and averaged k-point correlation of these matrices were universal
(and in particular, agreed with those for GUE) assuming additional regularity
hypotheses on the xℓk, yℓk. In [7], the other two authors, using a different method,
established the same conclusion assuming instead some moment and support conditions
on the xℓk, yℓk. In this short note we observe that the arguments of [3] and [7]
can be combined to establish universality of the gap distribution and averaged
k-point correlations for all Wigner matrices (with subexponentially decaying entries),
with no extra assumptions.@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: José
foaf_name: Ramírez, José A
foaf_surname: Ramírez
- foaf_Person:
foaf_givenName: Benjamin
foaf_name: Schlein, Benjamin
foaf_surname: Schlein
- foaf_Person:
foaf_givenName: Terence
foaf_name: Tao, Terence
foaf_surname: Tao
- foaf_Person:
foaf_givenName: Vu
foaf_name: Van, Vu
foaf_surname: Van
- foaf_Person:
foaf_givenName: Horng
foaf_name: Yau, Horng-Tzer
foaf_surname: Yau
bibo_issue: '4'
bibo_volume: 17
dct_date: 2010^xs_gYear
dct_publisher: International Press@
dct_title: Bulk universality for Wigner Hermitian matrices with subexponential decay@
...