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Explore the mathematical theory of Random Walks in Dynamic Random Environments through this 50-minute conference talk that addresses the complex mutual interactions between random walkers and their evolving environments. Learn about a novel criterion that enables the decomposition of random walker trajectories into independent and identically distributed increments, facilitating the establishment of limit theorems. Discover how this criterion involves constructing random fields with a Random Markov Property and developing decorrelation estimates. Examine the specific application to environments characterized by boolean percolation on $ \mathbb{Z}^{d}\times\mathbb{N}$, understanding how these mathematical structures influence walker behavior. Gain insights into collaborative research methodologies through work conducted with J. Allasia, R. Baldasso, and A. Teixeira. Access this presentation from the thematic meeting "Random walks: applications and interactions" held at the Centre International de Rencontres Mathématiques in Marseille, France, featuring enhanced viewing capabilities including chapter markers, keyword navigation, mathematical abstracts, bibliographies, and Mathematics Subject Classification for comprehensive study of this advanced probability theory topic.
