Cover Times for Brownian Motion and Random Walks in Two Dimensions

Let T(x,r) denote the first hitting time of the disc of radius r centered at x for Brownian motion on the two dimensional torus. We prove that sup_{x} T(x,r)/|log r|^2 --> 2/pi as r --> 0. The same applies to Brownian motion on any smooth, compact connected, two-dimensional, Riemannian manifol...

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Hauptverfasser:	Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Combinatorics Mathematics - Differential Geometry Mathematics - Probability
Online-Zugang:	Volltext bestellen
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