2016/03/11 by Tien‐Cuong Dinh, Dinh, Tien-Cuong, Viêt‐Anh Nguyên +1
Mathematics · #32U15 (32L05 #60F10) #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1603.03643
openalex publication_date 2016/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.