Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 25 (2020), paper no. 86, 14 pp.
Functional weak limit of random walks in cooling random environment
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.
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
Permanent link to this document
Digital Object Identifier
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