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arXiv · 1304.1446

Large Deviation For Outlying Coordinates in Beta Ensembles

Thomas Bloom
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Abstract

For Y a subset of the complex plane,a beta ensemble is a sequence of probability measures on Y^n 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 Y^n 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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Thomas Bloom. 2013-04-04. Large Deviation For Outlying Coordinates in Beta Ensembles. https://arxiv.org/abs/1304.1446

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