Berry-Esseen bound and Local Limit Theorem for the coefficients of products of random matrices

2021/10/18 by Tien‐Cuong Dinh, Dinh, Tien-Cuong, Lucas Kaufmann +3 · 1 citation
Mathematics · #37A30 #60B15 #60B20 #60F99 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2110.09032

openalex publication_date 2021/10/18 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28

Abstract

Let μ be a probability measure on GL_d(ℝ) and denote by S_n:= g_n ⋯ g₁ the associated random matrix product, where g_j are i.i.d. with law μ. Under the assumptions that μ has a finite exponential moment and generates a proximal and strongly irreducible semigroup, we prove a Berry-Esseen bound with the optimal rate O(1/√ n) and a general Local Limit Theorem for the coefficients of S_n.

Citations

• Products of Random Matrices

Cited by

• Limit theorems for the coefficients of random walks on the general linear group

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