Scaling limits of characteristic polynomials in classical beta ensembles
Speaker:Prof. Dang-Zheng Liu
Associate Professor
University of Science and Technology of China
Date & Time:10 Jun 2013 (Monday) 15:00
Venue:J213
Organized by:Department of Mathematics

Abstract

We study the local properties of eigenvalues for the Hermite (Gaussian), Laguerre (Chiral) and Jacobi beta-ensembles of random matrices. More specifically, we calculate scaling limits of the expectation value of products of characteristic polynomials in the bulk and at the edges of the spectrum of each beta-ensemble. All the asymptotic results rely on a generalization of Watson's lemma and the steepest descent method for integrals of Selberg type.

Biography

Prof. Dang-Zheng Liu received the B.S. degree in mathematics from Shaanxi Normal University (Xi'an), and the Ph.D. degree in mathematics from Peking University, Beijing. From October 2010 to August 2012, he worked as a postdoctoral researcher at the Universidad de Talca, Chile. In August 2012, he joined the School of Mathematical Sciences, University of Science and Technology of China, as an associate professor. His research focuses on random matrix theory. He is also interested in stochastic processes, multiple orthogonal polynomials and number theory related to random matrices.