Random walk on random walks: Higher dimensions
Authors
- Blondel, Oriane
- Hilário, Marcelo R.
- Soares dos Santos, Renato
- Sidoravicius, Vladas
- Teixeira, Augusto
2010 Mathematics Subject Classification
- 60F15 60K35 82B41 82C22 82C44
Keywords
- Random walk, dynamic random environment, law of large numbers, central limit theorem, large deviations, renormalization, regeneration
DOI
Abstract
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].
Appeared in
- Electron. J. Probab., 24 (2019), pp. 80/1-80/33.
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