Large deviations principle for some beta-ensembles
Abstract
Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on a weighted compact set in X, induces naturally a beta-ensemble, i.e., a random point process on the compact set. Physically, this general setting corresponds to a gas of free fermions in X and may admit some random matrix models. The empirical measures, associated with such beta-ensembles, converge almost surely to an equilibrium measure when p goes to infinity. We establish a large deviations principle (LDP) with an effective speed of convergence for these empirical measures. Our study covers the case of some beta-ensembles on a compact subset of a real sphere or of a real Euclidean space.
Cite
@article{arxiv.1603.03643,
title = {Large deviations principle for some beta-ensembles},
author = {Tien-Cuong Dinh and Viet-Anh Nguyen},
journal= {arXiv preprint arXiv:1603.03643},
year = {2016}
}
Comments
19 pages. arXiv admin note: text overlap with arXiv:1505.08050