Small deviations for beta ensembles

2009/12/26 by Michel Ledoux, Ledoux, Michel, Brian Rider +1 · 1 citation
Mathematics · #FOS: Mathematics #Mathematical functions and polynomials #Probability (math.PR) #Random Matrices and Applications #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.0912.5040

openalex publication_date 2009/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the distribution of the largest eigenvalue in principal components analysis

Cited by

• Large n-limit of matrix control problems and non-commutative controls

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• Large deviations for the extremal eigenvalues of Ginibre ensembles
• Limit Theorems for Beta-Jacobi Ensembles
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