2021/07/08 by Peter Eichelsbacher, Eichelsbacher, Peter, Benedikt Rednoß +1
Computer Science · Mathematics · #05C80 #60E10 #60F05 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2107.03775
openalex publication_date 2021/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In his work \citeTi80, Tikhomirov combined elements of Stein's method with the theory of characteristic functions to derive Kolmogorov bounds for the convergence rate in the central limit theorem for a normalized sum of a stationary sequence of random variables satisfying one of several weak dependency conditions. The combination of elements of Stein's method with the theory of characteristic functions is sometimes called Stein-Tikhomirov method. \citet*AMPS17 successfully used the Stein-Tikhomirov method to bound the convergence rate in contexts with non-Gaussian targets. \citet*Ro17 used the Stein-Tikhomirov method to bound the convergence rate in the Kolmogorov distance for normal approximation of normalized triangle counts in the Erdös-Rényi random graph.