Open Access
2022 Collisions of random walks in dynamic random environments
Noah Halberstam, Tom Hutchcroft
Author Affiliations +
Electron. J. Probab. 27: 1-18 (2022). DOI: 10.1214/21-EJP738


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.


We thank Sebastian Andres and Jonathan Hermon for helpful comments on a draft of the paper.


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Noah Halberstam. Tom Hutchcroft. "Collisions of random walks in dynamic random environments." Electron. J. Probab. 27 1 - 18, 2022.


Received: 4 January 2021; Accepted: 30 December 2021; Published: 2022
First available in Project Euclid: 17 January 2022

arXiv: 2009.13951
MathSciNet: MR4364738
zbMATH: 1511.60105
Digital Object Identifier: 10.1214/21-EJP738

Primary: 05C81 , 60J10 , 60K37 , 82C41

Keywords: Collisions , dynamic random environments , Dynamical percolation , Random walks

Vol.27 • 2022
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