Bulk scaling limit of the Laguerre ensemble

TL;DR

This paper proves that the bulk scaling limit of the beta-Laguerre ensemble exists for all positive beta and matches that of the beta-Hermite ensemble, extending understanding of eigenvalue distributions in random matrix theory.

Contribution

It establishes the existence and universality of the bulk scaling limit for the beta-Laguerre ensemble across all positive beta, linking it to the beta-Hermite ensemble.

Findings

Bulk scaling limit exists for all beta>0

Limit matches that of beta-Hermite ensemble

Extends universality in eigenvalue distributions

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.