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arXiv · 1801.03126

Schramm's formula for multiple loop-erased random walks

Adrien Poncelet
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Abstract

We revisit the computation of the discrete version of Schramm's formula for the loop-erased random walk derived by Kenyon. The explicit formula in terms of the Green function relies on the use of a complex connection on a graph, for which a line bundle Laplacian is defined. We give explicit results in the scaling limit for the upper half-plane, the cylinder and the Moebius strip. Schramm's formula is then extended to multiple loop-erased random walks.

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BibTeXRIS

Adrien Poncelet. 2018-01-09. Schramm's formula for multiple loop-erased random walks. https://doi.org/10.1088/1742-5468/aae5a6

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