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