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

Marius A. Schmidt

doi:10.1214/19-AOP1366

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Home > Journals > Ann. Probab. > Volume 48 > Issue 1 > Article

January 2020 A simple proof of the DPRZ theorem for 2d cover times

Marius A. Schmidt

Ann. Probab. 48(1): 445-457 (January 2020). DOI: 10.1214/19-AOP1366

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Abstract

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.

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Marius A. Schmidt. "A simple proof of the DPRZ theorem for 2d cover times." Ann. Probab. 48 (1) 445 - 457, January 2020. https://doi.org/10.1214/19-AOP1366