Bulk universality for Wigner Hermitian matrices with subexponential decay

L. Erdös, J. Ramírez, B. Schlein, T. Tao, V. Van, H. Yau, Mathematical Research Letters 17 (2010) 667–674.

Download
No fulltext has been uploaded. References only!
Journal Article | Published
Author
; ; ; ; ;
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.
Publishing Year
Date Published
2010-07-01
Journal Title
Mathematical Research Letters
Volume
17
Issue
4
Page
667 - 674
IST-REx-ID

Cite this

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.
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.
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 17, no. 4 (2010): 667–74.
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, pp. 667–674, 2010.
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.
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.

Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar