SLE on doubly-connected domains and the winding of loop-erased random walks
| dc.creator | Hagendorf, Christian | |
| dc.creator | Doussal, Pierre Le | |
| dc.date | 2008-03-22 | |
| dc.date.accessioned | 2026-07-07T10:12:48Z | |
| dc.date.available | 2026-07-07T10:12:48Z | |
| dc.description | Two-dimensional loop-erased random walks (LERWs) are random planar curves whose scaling limit is known to be a Schramm-Loewner evolution SLE_k with parameter k = 2. In this note, some properties of an SLE_k trace on doubly-connected domains are studied and a connection to passive scalar diffusion in a Burgers flow is emphasised. In particular, the endpoint probability distribution and winding probabilities for SLE_2 on a cylinder, starting from one boundary component and stopped when hitting the other, are found. A relation of the result to conditioned one-dimensional Brownian motion is pointed out. Moreover, this result permits to study the statistics of the winding number for SLE_2 with fixed endpoints. A solution for the endpoint distribution of SLE_4 on the cylinder is obtained and a relation to reflected Brownian motion pointed out. | |
| dc.description | 22 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0803.3249 | |
| dc.identifier | http://arxiv.org/abs/0803.3249 | |
| dc.identifier | J. Stat. Phys. 133 (2008) 231-254 | |
| dc.identifier | doi:10.1007/s10955-008-9614-z | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172309 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Mathematical Physics | |
| dc.title | SLE on doubly-connected domains and the winding of loop-erased random walks | |
| dc.type | text |