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March 2020 On the nature of the Swiss cheese in dimension $3$
Amine Asselah, Bruno Schapira
Ann. Probab. 48(2): 1002-1013 (March 2020). DOI: 10.1214/19-AOP1380

Abstract

We study scenarii linked with the Swiss cheese picture in dimension 3 obtained when two random walks are forced to meet often, or when one random walk is forced to squeeze its range. In the case of two random walks, we show that they most likely meet in a region of optimal density. In the case of one random walk, we show that a small range is reached by a strategy uniform in time. Both results rely on an original inequality estimating the cost of visiting sparse sites, and in the case of one random walk on the precise large deviation principle of van den Berg, Bolthausen and den Hollander (Ann. of Math. (2) 153 (2001) 355–406), including their sharp estimates of the rate functions in the neighborhood of the origin.

Citation

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Amine Asselah. Bruno Schapira. "On the nature of the Swiss cheese in dimension $3$." Ann. Probab. 48 (2) 1002 - 1013, March 2020. https://doi.org/10.1214/19-AOP1380

Information

Received: 1 July 2018; Revised: 1 January 2019; Published: March 2020
First available in Project Euclid: 22 April 2020

zbMATH: 07199867
MathSciNet: MR4089500
Digital Object Identifier: 10.1214/19-AOP1380

Subjects:
Primary: 60F10, 60G50

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 2 • March 2020
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