Open Access
November 2020 Symmetric exclusion as a random environment: Invariance principle
Milton Jara, Otávio Menezes
Ann. Probab. 48(6): 3124-3149 (November 2020). DOI: 10.1214/20-AOP1466


We establish an invariance principle for a one-dimensional random walk in a dynamic random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite box around the walker. The environment starts from equilibrium. After a suitable space-time rescaling, the random walk converges to a sum of two independent processes: a Brownian motion and a Gaussian process with stationary increments.


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Milton Jara. Otávio Menezes. "Symmetric exclusion as a random environment: Invariance principle." Ann. Probab. 48 (6) 3124 - 3149, November 2020.


Received: 1 July 2018; Revised: 1 May 2020; Published: November 2020
First available in Project Euclid: 20 October 2020

MathSciNet: MR4164462
Digital Object Identifier: 10.1214/20-AOP1466

Primary: 60K37 , 82C22
Secondary: 60F17

Keywords: Dynamic random environment , entropy estimates , Fluctuations , Random walk

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 6 • November 2020
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