Long time behaviour of random walks on the integer lattice

2015/12/30 by Bartosz Trojan, Trojan, Bartosz
Mathematics · Physics and Astronomy · #60B10 #60F05 #60F99 #60G50 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1512.09035

openalex publication_date 2015/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an irreducible finite range random walk on the d-dimensional integer lattice and study asymptotic behaviour of its transition function p(n; x). In particular, for simple random walk our asymptotic formula is valid as long as n (n - |x|₁)^-2 tends to zero.

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