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arXiv · 2003.10928

Loop-erased random walk as a spin system observable

Tyler Helmuth·Assaf Shapira
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Abstract

The determination of the Hausdorff dimension of the scaling limit of loop-erased random walk is closely related to the study of the one-point function of loop-erased random walk, i.e., the probability a loop-erased random walk passes through a given vertex. Recent work in the theoretical physics literature has investigated the Hausdorff dimension of loop-erased random walk in three dimensions by applying field theory techniques to study spin systems that heuristically encode the one-point function of loop-erased random walk. Inspired by this, we introduce two different spin systems whose correlation functions can be rigorously shown to encode the one-point function of loop-erased random walk.

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Tyler Helmuth, Assaf Shapira. 2020-03-24. Loop-erased random walk as a spin system observable. https://doi.org/10.1007/s10955-020-02628-7

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