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Collisions of random walks in dynamic random environments

Halberstam, Noah and Hutchcroft, Tom (2022) Collisions of random walks in dynamic random environments. Electronic Journal of Probability, 27 . Art. No. 8. ISSN 1083-6489. doi:10.1214/21-EJP738.

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We study dynamic random conductance models on ℤ² in which the environment evolves as a reversible Markov process that is stationary under space-time shifts. We prove under a second moment assumption that two conditionally independent random walks in the same environment collide infinitely often almost surely. These results apply in particular to random walks on dynamical percolation.

Item Type:Article
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URLURL TypeDescription Paper
Hutchcroft, Tom0000-0003-0061-593X
Additional Information:© 2022 Institute of Mathematical Statistics. Creative Commons Attribution 4.0 International License. Submitted to EJP on January 4, 2021, final version accepted on December 30, 2021. First available in Project Euclid: 17 January 2022. We thank Sebastian Andres and Jonathan Hermon for helpful comments on a draft of the paper.
Subject Keywords:Collisions, dynamic random environments, Dynamical percolation, Random walks
Classification Code:MSC 2020 subject classifications: 60J10; 05C81; 82C41; 60K37
Record Number:CaltechAUTHORS:20210924-202129801
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Official Citation:Noah Halberstam, Tom Hutchcroft "Collisions of random walks in dynamic random environments," Electronic Journal of Probability, Electron. J. Probab. 27, 1-18, (2022); DOI: 10.1214/21-EJP738
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111035
Deposited By: George Porter
Deposited On:27 Sep 2021 14:44
Last Modified:03 Feb 2022 21:03

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