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Detalles del recurso


Suppose that $\eta$ is a Schramm–Loewner evolution ( $\operatorname{SLE}_{\kappa}$ ) in a smoothly bounded simply connected domain $D\subset{\mathbf{C}}$ and that $\phi$ is a conformal map from $\mathbf{D}$ to a connected component of $D\setminus\eta([0,t])$ for some $t\gt 0$ . The multifractal spectrum of $\eta$ is the function $(-1,1)\to[0,\infty)$ which, for each $s\in(-1,1)$ , gives the Hausdorff dimension of the set of points $x\in\partial\mathbf{D}$ such that $|\phi'((1-\epsilon)x)|=\epsilon^{-s+o(1)}$ as $\epsilon\to0$ . We rigorously compute the almost sure multifractal spectrum of $\operatorname{SLE}$ , confirming a prediction due to Duplantier. As corollaries, we confirm a conjecture made by Beliaev and Smirnov for the almost sure bulk integral means spectrum of $\operatorname{SLE}$ , we obtain the optimal Hölder exponent for a conformal map which uniformizes the complement of an $\operatorname{SLE}$ curve, and we obtain a new derivation of the almost sure Hausdorff dimension of the $\operatorname{SLE}$ curve for $\kappa\leq4$ . Our results also hold for the $\operatorname{SLE}_{\kappa}(\underline{\rho})$ processes with general vectors of weight $\underline{\rho}$ .

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Project Euclid (Hosted at Cornell University Library)  


Gwynne, Ewain -  Miller, Jason -  Sun, Xin - 

Id.: 71215094

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveSchramm–Loewner evolution - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2018 Duke University Press

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0012-7094
[References] 1547-7398

Fecha de contribución: 14-abr-2018


* Duke Math. J. 167, no. 6 (2018), 1099-1237
* doi:10.1215/00127094-2017-0049

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