Annals of Probability

A simple proof of the DPRZ theorem for 2d cover times

Marius A. Schmidt

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We give a simple proof of the theorem by Dembo, Peres, Rosen and Zeitouni (DPRZ) regarding the time Brownian motion needs to cover every $\varepsilon$ ball on the two-dimensional unit torus in the $\varepsilon\searrow 0$ limit.

Article information

Ann. Probab., Volume 48, Number 1 (2020), 445-457.

Received: May 2018
Revised: February 2019
First available in Project Euclid: 25 March 2020

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Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65] 60G50: Sums of independent random variables; random walks 60G70: Extreme value theory; extremal processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Brownian motion multiscale analysis cover time hitting time


Schmidt, Marius A. A simple proof of the DPRZ theorem for 2d cover times. Ann. Probab. 48 (2020), no. 1, 445--457. doi:10.1214/19-AOP1366.

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