Continuous limits of Heterogeneous Continuous Time Random Walk model

TL;DR

This paper investigates the continuous limits of the Heterogeneous Continuous Time Random Walk model on networks, using generalized master equations to understand how different waiting time distributions influence the resulting continuous equations.

Contribution

It introduces a framework for deriving continuous equations from heterogeneous CTRW models on networks based on various waiting time interpretations.

Findings

Different forms of continuous equations are obtained depending on waiting time distribution interpretations.

The generalized master equation approach effectively models heterogeneous diffusion processes.

The study enhances understanding of diffusion in disordered media through network-based CTRW analysis.

Abstract

Continuous time random Walk model has been versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as disordered or porous media. We are studying the continuous limits of Heterogeneous Continuous Time Random Walk model, when a random walk is making jumps on a graph within different time-length. We apply the concept of a generalized master equation to study heterogeneous continuous-time random walks on networks. Depending on the interpretations of the waiting time distributions the generalized master equation gives different forms of continuous equations.