Small deviations for beta ensembles

By Michel Ledoux, Brian Rider. 2009

116 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/40d3676fd5dfb7c59f22aaf7023f9e62f218a2fd

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In Applied Mathematics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Edge Universality of Beta Ensembles (2013, methodology): “For the measures μ or μy, the tail probability of x1 has a slower decay exp [−C(γ1 − x1)] in the regime x1 ≪ γ1 in accordance with the tail behaviour of the Tracy-Widom law (for the Gaussian beta ensemble, see [40] for a detailed analysis of the edge tail behavior).”
Random matrices: Sharp concentration of eigenvalues (2012, unknown): “The GOE version of Theorem 11 follows from the results in [26].”
The directed landscape (2018, methodology): “t; a √ s) ≤ ce−da2. Finally, we will also need the ﬁnite versions of Theorem 2.3 and Lemma 2.4, as well as a proposition bounding the entire Brownian n-melon below a particular function. Theorem 2.5 (Ledoux and Rider (2010)). Let Wn 1 be the top line of a Brownian n-melon. There exist constants c an”