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Loop-erased random walk as a spin system observable.

Helmuth, Tyler and Shapira, Assaf (2020) 'Loop-erased random walk as a spin system observable.', Journal of statistical physics., 181 (4). pp. 1306-1322.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s10955-020-02628-7
Publisher statement:This is a post-peer-review, pre-copyedit version of a journal article published in the Journal of statistical physics. The final authenticated version is available online at: https://doi.org/10.1007/s10955-020-02628-7
Date accepted:17 August 2020
Date deposited:25 August 2020
Date of first online publication:24 August 2020
Date first made open access:24 August 2021

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