Local limit theorems for random walks on a large discrete torus

2024/11/06 by Y. T. Gu, Gu, Yandong, Dang-Zheng Liu +1
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2411.03634

openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by the study of edge statistics of random band matrices, we investigate random walks on large d-dimensional periodic lattices, whose transition matrices are determined by discretized density functions. Under certain moment assumption on the density, we prove local limit theorems for random walks in three different regimes according to the bandwidth parameter, random walk length and torus size.

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