Loop-erased random walk on finite graphs and the Rayleigh process
| dc.creator | Schweinsberg, Jason | |
| dc.date | 2006-11-06 | |
| dc.date | 2007-07-29 | |
| dc.date.accessioned | 2026-07-07T08:20:49Z | |
| dc.date.available | 2026-07-07T08:20:49Z | |
| dc.description | Let $(G_n)_{n=1}^{\infty}$ be a sequence of finite graphs, and let Y_t be the length of a loop-erased random walk on G_n after t steps. We show that for a large family of sequences of finite graphs, which includes the case in which G_n is the d-dimensional torus of size-length n for $d \geq 4$, the process $(Y_t)_{t=0}^{\infty}$, suitably normalized, converges to the Rayleigh process introduced by Evans, Pitman, and Winter. Our proof relies heavily on ideas of Peres and Revelle, who used loop-erased random walks to show that the uniform spanning tree on large finite graphs converges to the Brownian continuum random tree of Aldous. | |
| dc.identifier | https://arxiv.org/abs/math/0611155 | |
| dc.identifier | http://arxiv.org/abs/math/0611155 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135177 | |
| dc.subject | Probability | |
| dc.subject | 60G50 (Primary) 60K35, 60J75 (Secondary) | |
| dc.title | Loop-erased random walk on finite graphs and the Rayleigh process | |
| dc.type | text |