Research-Soft edge limit of the Laguerre beta-ensemble at the lower edge

Research

Probability & Statistics Seminar

Soft edge limit of the Laguerre beta-ensemble at the lower edge

Speaker: Jiaming Xu（The Ohio State University）
Time: Jun 8, 2026, 16:00-17:00
Location: M1001, College of Science Building

Abstract

The Laguerre beta-ensemble is an n-particle system on the real line with a parameter \beta>0 that generalizes the eigenvalue distribution of sample covariance matrices of dimension n and sample size (n+a). When “a” grows to infinity at any rate sublinear in “n”, the smallest eigenvalues are close to zero but strictly nonnegative, which leads to a potentially different behavior to the largest eigenvalues. We prove that, under appropriate scaling, these eigenvalues converge in distribution to the Airy (\beta) process, the universal edge limit for a large class of beta-ensembles.