Anomalous diffusion in random-walks with memory-induced relocations

TL;DR

This paper reviews how stochastic movement with memory-induced relocations affects transport properties, highlighting the impact of different relocation mechanisms on diffusion behavior in random walks.

Contribution

It formulates a general framework for random walks with memory, encompassing various specific cases like resets and relocations, to analyze their transport properties.

Findings

Relocation mechanisms can actively modify diffusion regimes.

Memory-driven relocations lead to anomalous diffusion behaviors.

The framework unifies different models of stochastic motion with memory.

Abstract

In this minireview we present the main results regarding the transport properties of stochastic movement with relocations to known positions. To do so, we formulate the problem in a general manner to see several cases extensively studied during the last years as particular situations within a framework of random walks with memory. We focus on (i) stochastic motion with resets to its initial position followed by a waiting period, and (ii) diffusive motion with memory-driven relocations to previously visited positions. For both of them we show how the overall transport regime may be actively modified by the details of the relocation mechanism.