The Effect of Finite Memory Cutoff on Loop Erased Walk in Z³

2004/11/24 by Wei-Shih Yang, Yang, Wei-Shih, Aklilu Zeleke +1
Mathematics · #60G50 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G50

paper · pdf · doi:10.48550/arxiv.math/0411551

10 pages

arxiv created 2004/11/24 · arxiv updated 2009/12/01

Abstract

Let ζbe the intersection exponent of random walks in Z³ and αbe a positive real number. We construct a stochastic process from a simple random walk by erasing loops of length at most N^α. We will prove that for α< (1)/(1+2ζ), the limiting distribution is Gaussian. For α> 2 the limiting distribution will be shown to be equal to the limiting distribution of the loop erased walk.

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