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

Wei-Shih Yang·Aklilu Zeleke
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Abstract

Let ζbe the intersection exponent of random walks in Z^3 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< \frac{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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Wei-Shih Yang, Aklilu Zeleke. 2004-11-24. The Effect of Finite Memory Cutoff on Loop Erased Walk in Z^3. https://arxiv.org/abs/math/0411551

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