Loop-Erased Random Walk as a Spin System Observable

Helmuth, Tyler; Shapira, Assaf

doi:10.1007/s10955-020-02628-7

Loop-Erased Random Walk as a Spin System Observable

Helmuth, Tyler; Shapira, Assaf

Authors

Dr Tyler Helmuth tyler.helmuth@durham.ac.uk
Associate Professor

Assaf Shapira

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.

Citation

Helmuth, T., & Shapira, A. (2020). Loop-Erased Random Walk as a Spin System Observable. Journal of Statistical Physics, 181(4), 1306-1322. https://doi.org/10.1007/s10955-020-02628-7

Journal Article Type	Article
Acceptance Date	Aug 17, 2020
Online Publication Date	Aug 24, 2020
Publication Date	2020-11
Deposit Date	Aug 25, 2020
Publicly Available Date	Aug 24, 2021
Journal	Journal of Statistical Physics
Print ISSN	0022-4715
Electronic ISSN	1572-9613
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	181
Issue	4
Pages	1306-1322
DOI	https://doi.org/10.1007/s10955-020-02628-7
Related Public URLs	https://arxiv.org/abs/2003.10928

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Copyright 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