Motivated by the random Lorentz gas, we study deterministic walks in random environment and show that (in simple, yet relevant cases) they can be reduced to a class of random walks in random environment where the jump probability depends (weakly) on the past. In addition, we prove few basic results (hopefully, the germ of a general theory) for the latter purely probabilistic model.
"Deterministic walks in random environment." Ann. Probab. 48 (5) 2212 - 2257, September 2020. https://doi.org/10.1214/19-AOP1421