Abstract

Random matrix theory has found many applications in physics, statistics and engineering since its inception. The eigenvalues of random matrices are often of particular interest. The standard technique for studying local eigenvalue behavior of a random matrix distribution involves the following steps. We first choose a family of n x n random matrices which we translate and rescale in order to focus on a particular region of the spectrum, and then we let n tend to infinity. When this procedure is performed carefully, the limiting eigenvalue behavior often falls into one of three classes: soft edge, hard edge or bulk. In the world of random matrices, three ensembles are of particular interest: the Hermite, Laguerre and Jacobi beta-ensembles. In this talk I will present a joint work with Benedek Valkó. We consider the beta-Laguerre ensemble, a family of distributions generalizing the joint eigenvalue distribution of the Wishart random matrices. We show that the bulk scaling limit of these ensembles exists for all beta > 0 for a general family of parameters and it is the same as the bulk scaling limit of the corresponding beta-Hermite ensemble.