Poncelet, Adrien
[UCL]
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.
Bibliographic reference |
Poncelet, Adrien. Schramm’s formula for multiple loop-erased random walks. In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2018, no.10, p. 103106 (2018) |
Permanent URL |
http://hdl.handle.net/2078.1/204491 |