Mesoscopic central limit theorem for general β-ensembles

2016/05/17 by Florent Bekerman, Bekerman, Florent, Asad Lodhia +1
Mathematics · #60B20 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1605.05206

openalex publication_date 2016/05/17 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We prove that the linear statistics of eigenvalues of β-log gasses satisfying the one-cut and off-critical assumption with a potential V ∈ C⁶(ℝ) satisfy a central limit theorem at all mesoscopic scales α∈ (0; 1). We prove this for compactly supported test functions f ∈ C⁵(ℝ) using loop equations at all orders along with rigidity estimates.

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