2016/12/19 by Jiaoyang Huang, Huang, Jiaoyang, Benjamin Landon +1
Economics, Econometrics and Finance · Mathematics · #15B52 #60F05 #82B44 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1612.06306
openalex publication_date 2016/12/19 · openalex created_date 2017/02/03 · openalex updated_date 2026/07/28
We study Dyson Brownian motion with general potential V and for general β≥ 1. For short times t = o (1) and under suitable conditions on V we obtain a local law and corresponding rigidity estimates on the particle locations; that is, with overwhelming probability, the particles are close to their classical locations with an almost-optimal error estimate. Under the condition that the density of states of the initial data is bounded below and above down to the scale η_* ≪ t ≪ 1, we prove a mesoscopic central limit theorem for linear statistics at all scales N-1≪η≪ t