| Título: | The Dimension of the Frontier of Planar Brownian Motion |
| Autores: | Lawler, Gregory F.; Duke University |
| Fecha: | 1996-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Mathematics Brownian motion, Hausdorff dimension, frontier, random fractals 60J65 |
| Descripción: | Let $B$ be a two dimensional Brownian motion and let the frontier of $B[0,1]$ be defined as the set of all points in $B[0,1]$ that are in the closure of the unbounded connected component of its complement. We prove that the Hausdorff dimension of the frontier equals $2(1 - \alpha)$ where $\alpha$ is an exponent for Brownian motion called the two-sided disconnection exponent. In particular, using an estimate on $\alpha$ due to Werner, the Hausdorff dimension is greater than $1.015$. |
| Idioma: | Inglés |
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