Mathematical Sciences Research Institute

Home » Gerard Ben Arous

Personal Profile of Dr. Gerard Ben Arous

Dr. Gerard Ben Arous

New York University, Courant Institute

Department of Mathematical Sciences

ORCID: https://orcid.org/0000-0001-5599-8726

MSRI Program:: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems
Visit Dates:: August 16, 2021 - December 15, 2021

Talks

September 13, 2010 - September 17, 2010

Workshop Random Matrix Theory and Its Applications I

Show All Collapse

Sep 14, 2010
Tuesday

11:30 AM - 12:10 PM		Extreme gaps in the spectrum of Random Matrices Gerard Ben Arous (New York University, Courant Institute)
Location -- Video Abstract I will present a joint work with Paul Bourgade (Harvard) about the extreme gaps between eigenvalues of random matrices. We give the joint limiting law of the smallest gaps for Haar-distributed unitary matrices (CUE) and matrices from the Gaussian Unitary Ensemble. In particular, we show that the smallest gaps when rescaled by N-4/3, are Poissonian and we give the limiting distribution of the kth smallest gap. We also show that the largest gap, when normalized by √log N/N, converges in L^p to a constant for all p > 0. These results are compared with the extreme gaps between zeros of the Riemann zeta function. Supplements -- Show Detail