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arXiv · 1603.03643

Large deviations principle for some beta-ensembles

Tien-Cuong Dinh·Viet-Anh Nguyen
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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.

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Tien-Cuong Dinh, Viet-Anh Nguyen. 2016-03-11. Large deviations principle for some beta-ensembles. https://arxiv.org/abs/1603.03643

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