Scaling limit of the step-reinforced and stochastic Levy--Lorentz model on weakly entangled integer lattice

Abstract

This paper describes the stochastic Levy--Lorentz gas driven by general long-range reference random walk on correlated and entangled random medium. Further consideration has been laid on the stochastic reinforcement of the underlying random walk, where it now possesses memory. Central limit theorems are obtained in both cases.