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**1 - 3**of**3**### THE SUBLEADING ORDER OF TWO DIMENSIONAL COVER TIMES

"... Abstract. The ε-cover time of the two dimensional torus by Brownian motion is the time it takes for the process to come within distance ε> 0 from any point. Its leading order in the small ε-regime has been established by Dembo, Peres, Rosen and Zeitouni [Ann. of Math., 160 (2004)]. In this work, ..."

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Abstract. The ε-cover time of the two dimensional torus by Brownian motion is the time it takes for the process to come within distance ε> 0 from any point. Its leading order in the small ε-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. David Belius1, Nicola Kistler2. 1.