All-time dynamics of continuous-time random walks on complex networks

TL;DR

This paper extends analytical methods to study the full-time dynamics of continuous-time random walks on complex networks, providing exact results for velocities, dispersions, and fluctuation theorems, crucial for understanding complex systems.

Contribution

It introduces an extended approach based on generalized master equations to analyze CTRW dynamics on complex networks, including lattices with branches and coupled chains.

Findings

Exact expressions for velocities and dispersions derived.

Generalized fluctuation theorems discussed for complex networks.

Method applicable to various complex network geometries.

Abstract

The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social and economic sciences. Recently, several theoretical approaches have been developed that allowed to analyze explicitly dynamics of CTRW at all times, which is critically important for understanding mechanisms of underlying phenomena. However, theoretical analysis has been done mostly for systems with a simple geometry. Here we extend the original method based on generalized master equations to analyze all-time dynamics of CTRW models on complex networks. Specific calculations are performed for models on lattices with branches and for models on coupled parallel-chain lattices. Exact expressions for velocities and dispersions are obtained. Generalized fluctuations theorems for CTRW models on complex networks are discussed.