Large Deviation For Outlying Coordinates in Beta Ensembles
Probability
2014-01-14 v3
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.
Cite
@article{arxiv.1304.1446,
title = {Large Deviation For Outlying Coordinates in Beta Ensembles},
author = {Thomas Bloom},
journal= {arXiv preprint arXiv:1304.1446},
year = {2014}
}
Comments
26 pages,new section on Bernstein-Markov measures.Version to appear in Journal of Approximation Theory