On Universality of Bulk Local Regime of the Deformed Laguerre Ensemble

Abstract

We consider the deformed Laguerre Ensemble $H_n=\frac{1}{m}{\Sigma }_n^{1/2}{A}_{m,n}{A}_{m,n}^{\ast }{\Sigma }_n^{1/2}$ in which ${\Sigma }_n$ is a positive hermitian matrix (possibly random) and $A_{m,n}$ is a $n\times m$ complex Gaussian random matrix (independent of ${\Sigma }_n$), $\frac{m}{n}\to c>1$. Assuming that the Normalized Counting Measure of ${\Sigma }_n$ converges weakly (in probability) to a non-random measure $N^{(0)}$ with a bounded support we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of $H_n$.

27 pages, 3 figures

References in corpus (2)

• Random matrices: Universality of local eigenvalue statistics
• Bulk Universality for Wigner Matrices