Local Central Limit Theorem for a Random Walk Perturbed in One Point

2016/05/20 by Genovese, Giuseppe, Lucà, Renato
#60F05 #60G50 #60J10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1605.06227

Abstract

We consider a symmetric random walk on the ν-dimensional lattice, whose exit probability from the origin is modified by an antisymmetric perturbation and prove the local central limit theorem for this process. A short-range correction to diffusive behaviour appears in any dimension along with a long-range correction in the one-dimensional case.

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