2025/11/07 by Charlie Dworaczek Guera, Guera, Charlie Dworaczek, Ronan Memin +3 · 1 citation
Mathematics · #46B09 #52A23 #60B20 #60F05 #FOS: Mathematics #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods #Metric Geometry (math.MG) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2511.05386
openalex publication_date 2025/11/07 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28
In this paper, we are interested in the β-ensembles (or 1D log-gas) with Freud weights, namely with a potential of the form |x|p with p ≥ 2. Since this potential is not of class C3 when p ∈ (2,3], most of the literature does not apply. In this singular setting, we prove a central limit theorem for linear statistics with general test-functions. Our strategy relies on establishing an optimal local law in the spirit of [Bourgade, Mody, Pain 22'. Our results allow us to give a consistency check of the KLS conjecture for the uniform distributions on p-Schatten balls and the functions f(X)=Tr(Xr)q. While the case p>3, q=1, r=2 was proven in [Dadoun, Fradelizi, Guédon, Zitt 23'], we address in the present paper the case p≥2, q≥1 and r≥2 an even integer. The proofs are based on a link between the moments of norms of uniform laws on p-Schatten balls and the β-ensembles with Freud weights.