| Título: | Brownian Motion on Compact Manifolds: Cover Time and Late Points |
| Autores: |
Dembo, Amir; Stanford University Peres, Yuval; University of California, Berkeley Rosen, Jay; College of Staten Island, CUNY |
| Fecha: | 2003-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Brownian motion, manifold, cover time, Wiener sausage. 60J65 |
| Descripción: | Let $M$ be a smooth, compact, connected Riemannian manifold of dimension $d>2$ and without boundary. Denote by $T(x,r)$ the hitting time of the ball of radius $r$ centered at $x$ by Brownian motion on $M$. Then, $C_r(M)=\sup_{x \in M} T(x,r)$ is the time it takes Brownian motion to come within $r$ of all points in $M$. We prove that $C_r(M)/(r^{2-d}|\log r|)$ tends to $\gamma_d V(M)$ almost surely as $r\to 0$, where $V(M)$ is the Riemannian volume of $M$. We also obtain the ``multi-fractal spectrum'' $f(\alpha)$ for ``late points'', i.e., the dimension of the set of $\alpha$-late points $x$ in $M$ for which $\limsup_{r\to 0} T(x,r)/ (r^{2-d}|\log r|) = \alpha >0$. |
| Idioma: | No aplica |
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