The Effect of Finite Memory Cutoff on Loop Erased Walk in Z^3
Probability
2007-05-23 v1
Abstract
Let \zeta be the intersection exponent of random walks in Z^3 and \alpha be a positive real number. We construct a stochastic process from a simple random walk by erasing loops of length at most N^\alpha. We will prove that for \alpha < \frac{1}{1+2\zeta}, the limiting distribution is Gaussian. For \alpha > 2 the limiting distribution will be shown to be equal to the limiting distribution of the loop erased walk.
Keywords
Cite
@article{arxiv.math/0411551,
title = {The Effect of Finite Memory Cutoff on Loop Erased Walk in Z^3},
author = {Wei-Shih Yang and Aklilu Zeleke},
journal= {arXiv preprint arXiv:math/0411551},
year = {2007}
}
Comments
10 pages