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2020 Functional weak limit of random walks in cooling random environment
Yongjia Xie
Electron. Commun. Probab. 25: 1-14 (2020). DOI: 10.1214/20-ECP360

Abstract

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.

Citation

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Yongjia Xie. "Functional weak limit of random walks in cooling random environment." Electron. Commun. Probab. 25 1 - 14, 2020. https://doi.org/10.1214/20-ECP360

Information

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

Digital Object Identifier: 10.1214/20-ECP360

Subjects:
Primary: 60F17, 60G50, 60K37

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