The subleading order of two dimensional cover times

Abstract

The epsilon-cover time of the two dimensional torus by Brownian motion is the time it takes for the process to come within distance epsilon>0 from any point. Its leading order in the small epsilon-regime has been established by Dembo, Peres, Rosen and Zeitouni [Ann. of Math., 160 (2004)]. In this work, the second order correction is identified. The approach relies on a multi-scale refinement of the second moment method, and draws on ideas from the study of the extremes of branching Brownian motion.

72 pages, 6 figures

References in corpus (1)

• A sharp estimate for cover times on binary trees

Cited by in corpus (2)

• Derrida's random energy models. From spin glasses to the extremes of correlated random fields
• Maximum and minimum of local times for two-dimensional random walk