The Effect of Finite Memory Cutoff on Loop Erased Walk in Z^3

Details The Effect of Finite Memory Cutoff on Loop Erased Walk in Z^3 The Effect of Finite Memory Cutoff on Loop Erased Walk in Z^3

2004-11-24

arxiv.org/abs/math/0411551v1

Mathematics

Probability

10 pages

Scientific paper

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.

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