Bulk Scaling Limit of the Laguerre Ensemble

Abstract

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.