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We are interested in Random Walks in Dynamic Random Environments. The main difficulty in the study of these systems is the strong mutual interaction between the walker and its environment. We propose a criterion that, when satisfied, allows to decompose the random walker trajectory into iid increments and in turn to establish limit theorems. The criterion concerns the environment and involves constructing a random field satisfying what we call a Random Markov Property, as well as decorrelation estimates. In this talk we focus on an environment given by boolean percolation on $ \mathbb{Z}^{d}\times\mathbb{N}$. Based on joint work with J. Allasia, R. Baldasso et A. Teixeira. Recording during the thematic meeting : «Random walks: applications and interactions» the January 20, 2026 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area