## Annals of Probability

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

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

#### 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.

#### Article information

**Source**

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

**Dates**

Received: May 2018

Revised: February 2019

First available in Project Euclid: 25 March 2020

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1585123334

**Digital Object Identifier**

doi:10.1214/19-AOP1366

**Mathematical Reviews number (MathSciNet)**

MR4079442

**Zentralblatt MATH identifier**

07206764

**Subjects**

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]

**Keywords**

Brownian motion multiscale analysis cover time hitting time

#### Citation

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. https://projecteuclid.org/euclid.aop/1585123334