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August 2020 Random walk on random walks: Low densities
Oriane Blondel, Marcelo R. Hilário, Renato S. dos Santos, Vladas Sidoravicius, Augusto Teixeira
Ann. Appl. Probab. 30(4): 1614-1641 (August 2020). DOI: 10.1214/19-AAP1537

Abstract

We consider a random walker in a dynamic random environment given by a system of independent discrete-time simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on particles. Surprisingly, the random walker may behave very differently depending on whether the underlying environment particles perform lazy or nonlazy random walks, which is related to a notion of permeability of the system. We also provide a strong law of large numbers, a functional central limit theorem and large deviation bounds under an ellipticity condition.

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Oriane Blondel. Marcelo R. Hilário. Renato S. dos Santos. Vladas Sidoravicius. Augusto Teixeira. "Random walk on random walks: Low densities." Ann. Appl. Probab. 30 (4) 1614 - 1641, August 2020. https://doi.org/10.1214/19-AAP1537

Information

Received: 1 October 2017; Revised: 1 June 2019; Published: August 2020
First available in Project Euclid: 4 August 2020

MathSciNet: MR4132636
Digital Object Identifier: 10.1214/19-AAP1537

Subjects:
Primary: 60F15 , 60K35 , 60K37
Secondary: 82B41 , 82C22 , 82C44

Keywords: Dynamic random environment , functional central limit theorem , large deviation bound , Random walk , Regeneration times , renormalisation , Strong law of large numbers

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 4 • August 2020
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