2017/05/30 by Valentin Féray, Féray, Valentin, Pierre‐Loïc Méliot +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Field-Flow Fractionation Techniques #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1705.10485
openalex publication_date 2017/05/30 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
In this paper, we give estimates for the speed of convergence towards a limiting stable law in the recently introduced setting of mod-ϕ convergence. Namely, we define a notion of zone of control, closely related to mod-ϕ convergence, and we prove estimates of Berry-Esseen type under this hypothesis. Applications include: the winding number of a planar Brownian motion; classical approximations of stable laws by compound Poisson laws; examples stemming from determinantal point processes (characteristic polynomials of random matrices and zeroes of random analytic functions); sums of variables with an underlying dependency graph (for which we recover a result of Rinott, obtained by Stein's method); the magnetization in the d-dimensional Ising model; and functionals of Markov chains.