| Título: | Intersection probabilities for a chordal SLE path and a semicircle |
| Autores: |
Alberts, Tom; New York University Kozdron, Michael J; University of Regina |
| Fecha: | 2008-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Schramm-Loewner evolution; restriction property; Hausdorff dimension; swallowing time; intersection probability; Schwarz-Christoffel transformation 82B21; 60K35; 60G99; 60J65 |
| Descripción: | We derive a number of estimates for the probability that a chordal SLE$_\kappa$ path in the upper half plane $\mathbb{H}$ intersects a semicircle centred on the real line. We prove that if $0<\kappa <8$ and $\gamma:[0,\infty) \to \overline{\mathbb{H}}$ is a chordal SLE$_\kappa$ in $\mathbb{H}$ from $0$ to $\infty$, then $P\{\gamma[0,\infty) \cap \mathcal{C}(x;rx) \neq \emptyset\} \asymp r^{4a-1}$ where $a=2/\kappa$ and $\mathcal{C}(x;rx)$ denotes the semicircle centred at $x>0$ of radius $rx$, $00$. 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$_\kappa$ path in $\mathbb{H}$ from $0$ to $\infty$. |
| Idioma: | No aplica |
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