The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torus
| dc.creator | Schweinsberg, Jason | |
| dc.date | 2006-02-23 | |
| dc.date | 2007-07-29 | |
| dc.date.accessioned | 2026-07-07T08:20:48Z | |
| dc.date.available | 2026-07-07T08:20:48Z | |
| dc.description | Let x and y be points chosen uniformly at random from $\Z_n^4$, the four-dimensional discrete torus with side length n. We show that the length of the loop-erased random walk from x to y is of order $n^2 (\log n)^{1/6}$, resolving a conjecture of Benjamini and Kozma. We also show that the scaling limit of the uniform spanning tree on $\Z_n^4$ is the Brownian continuum random tree of Aldous. Our proofs use the techniques developed by Peres and Revelle, who studied the scaling limits of the uniform spanning tree on a large class of finite graphs that includes the d-dimensional discrete torus for $d \geq 5$, in combination with results of Lawler concerning intersections of four-dimensional random walks. | |
| dc.description | A few typos and minor errors corrected, some proofs simplified | |
| dc.identifier | https://arxiv.org/abs/math/0602515 | |
| dc.identifier | http://arxiv.org/abs/math/0602515 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135171 | |
| dc.subject | Probability | |
| dc.subject | 60G50 (Primary) 60K35, 60D05 (Secondary) | |
| dc.title | The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torus | |
| dc.type | text |