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.
Citation
Michel Ledoux. Brian Rider. "Small Deviations for Beta Ensembles." Electron. J. Probab. 15 1319 - 1343, 2010. https://doi.org/10.1214/EJP.v15-798
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