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arXiv · 2409.12515

Random Markov property for random walks in random environments

Julien Allasia·Rangel Baldasso·Oriane Blondel·Augusto Teixeira
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Abstract

We consider random walks in dynamic random environments and propose a criterion which, if satisfied, allows to decompose the random walk trajectory into i.i.d. increments, and ultimately to prove limit theorems. The criterion involves the construction of a random field built from the environment, that has to satisfy a certain random Markov property along with some mixing estimates. We apply this criterion to correlated environments such as Boolean percolation and renewal chains featuring polynomial decay of correlations.

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Julien Allasia, Rangel Baldasso, Oriane Blondel, Augusto Teixeira. 2024-09-19. Random Markov property for random walks in random environments. https://arxiv.org/abs/2409.12515

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