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

TL;DR

This paper investigates the scaling limits of a stochastic Levy--Lorentz model with reinforcement on a complex entangled lattice, establishing central limit theorems for both reinforced and non-reinforced cases.

Contribution

It introduces a new analysis of the Levy--Lorentz model with stochastic reinforcement and derives central limit theorems for these processes.

Findings

Central limit theorems established for reinforced and non-reinforced models

Analysis of the impact of long-range correlations on scaling limits

Extension to entangled and correlated random media

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.