50:36
published on February 6, 2026
On some deterministic version of the random walk on $\mathbb{Z}^d$
By Dalia Terhesiu
Random walks in dynamic random environment
Appears in collection : Random walks: applications and interactions / Marches aléatoires: applications et interactions
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.
