Conformal restriction: the chordal case
| dc.creator | Lawler, Gregory | |
| dc.creator | Schramm, Oded | |
| dc.creator | Werner, Wendelin | |
| dc.date | 2002-09-25 | |
| dc.date | 2003-04-25 | |
| dc.date.accessioned | 2026-07-07T10:58:55Z | |
| dc.date.available | 2026-07-07T10:58:55Z | |
| dc.description | We characterize and describe all random subsets $K$ of a given simply connected planar domain (the upper half-plane $\H$, say) which satisfy the ``conformal restriction'' property, i.e., $K$ connects two fixed boundary points (0 and $\infty$, say) and the law of $K$ conditioned to remain in a simply connected open subset $D$ of $\H$ is identical to that of $Φ(K)$, where $Φ$ is a conformal map from $\H$ onto $D$ with $Φ(0)=0$ and $Φ(\infty)=\infty$. The construction of this family relies on the stochastic Loewner evolution (SLE) processes with parameter $κ\le 8/3$ and on their distortion under conformal maps. We show in particular that SLE(8/3) is the only random simple curve satisfying conformal restriction and relate it to the outer boundaries of planar Brownian motion and SLE(6). | |
| dc.description | To appear in JAMS | |
| dc.identifier | https://arxiv.org/abs/math/0209343 | |
| dc.identifier | http://arxiv.org/abs/math/0209343 | |
| dc.identifier | J.Am.Math.Soc.16:917-955,2003 | |
| dc.identifier | doi:10.1090/S0894-0347-03-00430-2 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/187273 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | Complex Variables | |
| dc.subject | 60D05; 60J65; 30C99 | |
| dc.title | Conformal restriction: the chordal case | |
| dc.type | text |