Random Walk on Lattice with an Antisymmetric Perturbation in One Point

2012/08/26 by Giuseppe Genovese, Renato Lucà, Genovese, Giuseppe +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #60G50 #Diffusion and Search Dynamics #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR #msc:60G50

paper · pdf · doi:10.48550/arxiv.1208.5239

This paper has been withdrawn by the author due to a error in the proof

openalex publication_date 2012/08/26 · arxiv created 2016/05/21 · arxiv updated 2016/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study an homogeneous irreducible markovian random walk in a square lattice of arbitrary dimension, with an antisymmetric perturbation acting only in one point. We compute exactly spatial correction to the diffusive behaviour in the asympotics of probability, in the spirit of local limit theorems for random walks.

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