Schramm’s formula for multiple loop-erased random walks

Poncelet, Adrien
(2018) Journal of Statistical Mechanics: Theory and Experiment — Vol. 2018, n° 10, p. 103106 (2018)

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  • Poncelet, AdrienUCLouvain
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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 Möbius strip. Schramm's formula is then extended to multiple loop-erased random walks.
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Poncelet, A. (2018). Schramm’s formula for multiple loop-erased random walks. Journal of Statistical Mechanics: Theory and Experiment, 2018(10), 103106. https://doi.org/10.1088/1742-5468/aae5a6 (Original work published 2018)