Large Deviation For Outlying Coordinates in Beta Ensembles

2013/04/04 by Thomas Bloom, Bloom, Thomas
Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1304.1446

openalex publication_date 2013/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For Y a subset of the complex plane,a beta ensemble is a sequence of probability measures on Yⁿ for n=1,2,3...depending on a real-valued continuous function Q and a real positive parameter beta.We consider the associated sequence of probability measures on Y where the probability of a subset W is given by the probability that at least one coordinate of Yⁿ belongs to W. With appropriate restrictions on Y,Q we prove a large deviation principle for this sequence of measures. This extends a result of Borot-Guionnet to subsets of the complex plane and to beta ensembles defined with measures using a Bernstein-Markov condition.

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