English

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.

Keywords

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

R2 v1 2026-06-21T23:54:02.926Z