Small deviations for beta ensembles
Michel Ledoux, Brian Rider
TL;DR
This paper derives small deviation inequalities for the extremal eigenvalues at the soft edge of beta ensembles, providing bounds on their variance and enhancing understanding of their probabilistic behavior.
Contribution
It introduces new small deviation inequalities for extremal eigenvalues in beta-Hermite and beta-Laguerre ensembles, with immediate variance bounds.
Findings
Upper bounds on the variance of the largest eigenvalue
Small deviation inequalities established for extremal eigenvalues
Enhanced probabilistic understanding of beta ensembles
Abstract
We establish various small deviation inequalities for the extremal (soft edge) eigenvalues in the beta-Hermite and beta-Laguerre ensembles. In both settings, upper bounds on the variance of the largest eigenvalue of the anticipated order follow immediately.
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Taxonomy
TopicsRandom Matrices and Applications · Mathematical functions and polynomials · Spectral Theory in Mathematical Physics