---
_id: '2763'
abstract:
- lang: eng
text: 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.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: José
full_name: Ramírez, José A
last_name: Ramírez
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- first_name: Terence
full_name: Tao, Terence
last_name: Tao
- first_name: Vu
full_name: Van, Vu
last_name: Van
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
citation:
ama: Erdös L, Ramírez J, Schlein B, Tao T, Van V, Yau H. Bulk universality for Wigner
Hermitian matrices with subexponential decay. *Mathematical Research Letters*.
2010;17(4):667-674.
apa: Erdös, L., Ramírez, J., Schlein, B., Tao, T., Van, V., & Yau, H. (2010).
Bulk universality for Wigner Hermitian matrices with subexponential decay. *Mathematical
Research Letters*. International Press.
chicago: Erdös, László, José Ramírez, Benjamin Schlein, Terence Tao, Vu Van, and
Horng Yau. “Bulk Universality for Wigner Hermitian Matrices with Subexponential
Decay.” *Mathematical Research Letters*. International Press, 2010.
ieee: L. Erdös, J. Ramírez, B. Schlein, T. Tao, V. Van, and H. Yau, “Bulk universality
for Wigner Hermitian matrices with subexponential decay,” *Mathematical Research
Letters*, vol. 17, no. 4. International Press, pp. 667–674, 2010.
ista: Erdös L, Ramírez J, Schlein B, Tao T, Van V, Yau H. 2010. Bulk universality
for Wigner Hermitian matrices with subexponential decay. Mathematical Research
Letters. 17(4), 667–674.
mla: Erdös, László, et al. “Bulk Universality for Wigner Hermitian Matrices with
Subexponential Decay.” *Mathematical Research Letters*, vol. 17, no. 4, International
Press, 2010, pp. 667–74.
short: L. Erdös, J. Ramírez, B. Schlein, T. Tao, V. Van, H. Yau, Mathematical Research
Letters 17 (2010) 667–674.
date_created: 2018-12-11T11:59:28Z
date_published: 2010-07-01T00:00:00Z
date_updated: 2021-01-12T06:59:32Z
day: '01'
extern: 1
intvolume: ' 17'
issue: '4'
month: '07'
page: 667 - 674
publication: Mathematical Research Letters
publication_status: published
publisher: International Press
publist_id: '4129'
quality_controlled: 0
status: public
title: Bulk universality for Wigner Hermitian matrices with subexponential decay
type: journal_article
volume: 17
year: '2010'
...