Intersection probabilities for a chordal SLE path and a semicircle
| dc.creator | Alberts, Tom | |
| dc.creator | Kozdron, Michael J. | |
| dc.date | 2007-07-20 | |
| dc.date | 2008-03-07 | |
| dc.date.accessioned | 2026-07-07T13:14:14Z | |
| dc.date.available | 2026-07-07T13:14:14Z | |
| dc.description | We derive a number of estimates for the probability that a chordal SLE path in the upper half plane H intersects a semicircle centred on the real line. We prove that if 0<kappa<8 and gamma:[0,infinity) to closure(H) is a chordal SLE in H from 0 to infinity, then P(gamma[0,infinity) cap C(x;rx) neq emptyset) asymp r^(4a-1) where a=2/kappa and C(x;rx) denotes the semicircle centred at x>0 of radius rx, 0<r<1/3, in the upper half plane. As an application of our results, for 0<kappa<8, we derive an estimate for the diameter of a chordal SLE path in H between two real boundary points 0 and x>0. For 4<kappa<8, we also estimate the probability that an entire semicircle on the real line is swallowed at once by a chordal SLE path in H from 0 to infinity. | |
| dc.description | v2: 11 pages, 7 figures; changed title, fixed typos, shortened some proofs, updated acknowledgements and references | |
| dc.identifier | https://arxiv.org/abs/0707.3163 | |
| dc.identifier | http://arxiv.org/abs/0707.3163 | |
| dc.identifier | Electron. Comm. Probab., volume 13, paper 43, pages 448-460, 2008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230143 | |
| dc.subject | Probability | |
| dc.subject | 82B21 (Primary), 60K35, 60G99, 60J65 (Secondary) | |
| dc.title | Intersection probabilities for a chordal SLE path and a semicircle | |
| dc.type | text |