Electronic Communications in Probability

Functional weak limit of random walks in cooling random environment

Yongjia Xie

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We prove an annealed weak limit of the trajectory of the random walks in cooling random environment (RWCRE) under both slow (polynomial) and fast (exponential) cooling. We identify the weak limit when the underlying static environment is recurrent (Sinai’s model). Avena and den Hollander have previously proved a Gaussian limiting distribution for the distribution of the endpoint of the walk. We find that the weak limit of the trajectory exists as a time-rescaled Brownian motion in the slow cooling case but the limit degenerates to a constant function in the fast cooling one.

Article information

Electron. Commun. Probab., Volume 25 (2020), paper no. 86, 14 pp.

Received: 11 October 2019
Accepted: 6 November 2020
First available in Project Euclid: 30 December 2020

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Primary: 60F17: Functional limit theorems; invariance principles 60G50: Sums of independent random variables; random walks 60K37: Processes in random environments

random walk dynamic random environment resampling times functional weak limit

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Xie, Yongjia. Functional weak limit of random walks in cooling random environment. Electron. Commun. Probab. 25 (2020), paper no. 86, 14 pp. doi:10.1214/20-ECP360. https://projecteuclid.org/euclid.ecp/1609319091

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