| Título: | On the most visited sites of planar Brownian motion |
| Autores: |
Cammarota, Valentina; "Sapienza" University of Rome Mörters, Peter; University of Bath |
| Fecha: | 2012-01-02 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Brownian motion, Hausdorff dimension, Hausdorff gauge, local time, point of infinite multiplicity, uniform dimension estimates. 60J65 |
| Descripción: | Let $(B_t \colon t \ge 0)$ be a planar Brownian motion and define gauge functions $\phi_\alpha(s)=\log(1/s)^{-\alpha}$ for $\alpha>0$. If $\alpha<1$ we show that almost surely there exists a point $x$ in the plane such that ${\mathcal H}^{\phi_\alpha}(\{t \ge 0 \colon B_t=x\})>0$,but if $\alpha>1$ almost surely ${\mathcal H}^{\phi_\alpha} (\{t \ge 0 \colon B_t=x\})=0$ simultaneously for all $x\in{\mathbb R}^2$. This resolves a longstanding open problem posed by S.J. Taylor in 1986. |
| Idioma: | Inglés |
1 On the Non-Convexity of the Time Constant in First-Passage Percolation por Kesten, Harry; Cornell University | 6 Simulations and Conjectures for Disconnection Exponents por Puckette, Emily E.; Occidental College,Werner, Wendelin; Université Paris-Sud and IUF |
2 A Proof of a Conjecture of Bobkov and Houdré por Kwapien, S.; Warsaw University,Pycia, M.; Warsaw University,Schachermayer, W.; University of Vienna | 7 Excursions Into a New Duality Relation for Diffusion Processes por Jansons, Kalvis M.; University College London |
3 Moderate Deviations for Martingales with Bounded Jumps por Dembo, Amir; Stanford University | 8 Percolation Beyond $Z^d$, Many Questions And a Few Answers por Benjamini, Itai; Weizmann Institute of Science,Schramm, Oded; Microsoft Research |
4 Bounds for Disconnection Exponents por Werner, Wendelin; Université Paris-Sud and IUF | 9 Transportation Approach to Some Concentration Inequalities in Product Spaces por Dembo, Amir; Stanford University,Zeitouni, Ofer; Technion - Israel Institute of Technology |
5 The Dimension of the Frontier of Planar Brownian Motion por Lawler, Gregory F.; Duke University | 10 Surface Stretching for Ornstein Uhlenbeck Velocity Fields por Carmona, Rene; Princeton University,Grishin, Stanislav; Princeton University,Xu, Lin; Princeton University,Molchanov, Stanislav; University of North Carolina at Charlotte |