Thu, April 2, 2026
10:20 am - 11:15 am
Math Tower (MW) 154
Jiaming Xu
The Ohio State University
Title
Airy limit at the hard edge of Laguerre beta-ensemble
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 the so-called hard edge behavior. 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.