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Random Markov property for random walks in random environ...
[Submitted on 19 Sep 2024 (v1), last revised 21 Aug 2026 (this v · 2024-09-19 · via math updates on arXiv.org

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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.

Submission history

From: Oriane Blondel [view email]
[v1] Thu, 19 Sep 2024 07:13:02 UTC (35 KB)
[v2] Fri, 21 Aug 2026 12:34:14 UTC (39 KB)