학술논문
Tightness for the cover time of the two dimensional sphere.
Document Type
Journal
Author
Belius, David (CH-BASL-MCS) AMS Author Profile; Rosen, Jay (1-CUNYS) AMS Author Profile; Zeitouni, Ofer (IL-WEIZ-NDM) AMS Author Profile
Source
Subject
60 Probability theory and stochastic processes -- 60J Markov processes
60J65Brownian motion
60J65
Language
English
Abstract
Summary: ``Let $\Cal C\sp*_{\epsilon,\bold S^2}$ denote the cover time of the two dimensional sphere by a Wiener sausage of radius $\epsilon$. We prove that $$ \sqrt{\Cal C\sp*_{\epsilon,\bold S^2}}-\sqrt{\frac{2A_{\bold S^2}} {\pi}}\left(\log \epsilon^{-1}-\frac 14\log\log^{-1}\right) $$ is tight, where $A_{\bold S^2}=4\pi$ denotes the Riemannian area of $\bold S^2$.''