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2019 Random walk on random walks: higher dimensions
Oriane Blondel, Marcelo R. Hilário, Renato S. dos Santos, Vladas Sidoravicius, Augusto Teixeira
Electron. J. Probab. 24: 1-33 (2019). DOI: 10.1214/19-EJP337


We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition kernels without the assumption of uniform ellipticity or nearest-neighbour jumps. Specifically, we obtain a strong law of large numbers, a functional central limit theorem and large deviation estimates for the position of the random walker under the annealed law in a high density regime. The main obstacle is the intrinsic lack of monotonicity in higher-dimensional, non-nearest neighbour settings. Here we develop more general renormalization and renewal schemes that allow us to overcome this issue. As a second application of our methods, we provide an alternative proof of the ballistic behaviour of the front of (the discrete-time version of) the infection model introduced in [23].


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Oriane Blondel. Marcelo R. Hilário. Renato S. dos Santos. Vladas Sidoravicius. Augusto Teixeira. "Random walk on random walks: higher dimensions." Electron. J. Probab. 24 1 - 33, 2019.


Received: 23 October 2017; Accepted: 21 June 2019; Published: 2019
First available in Project Euclid: 5 September 2019

zbMATH: 07107387
MathSciNet: MR4003133
Digital Object Identifier: 10.1214/19-EJP337

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


Vol.24 • 2019
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