Random walk on disordered networks

TL;DR

This paper investigates how disorder and curvature in cellular networks affect random walk diffusion, revealing enhanced short-term displacement and altered long-term behavior, with implications for understanding diffusion on curved spaces.

Contribution

It provides a detailed analysis of random walks on disordered curved networks, deriving evolution coefficients and linking diffusion to hyperbolic Brownian motion.

Findings

Disorder enhances short-time mean square displacement.

Long-time displacement is suppressed compared to ordered systems.

Diffusion on hyperbolic lattices relates to hyperbolic Brownian motion.

Abstract

Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The effects of disorder and space-curvature on the diffusion phenomena are investigated. In disordered systems the mean square displacement displays an enhancement at short time and a lowering at long ones, with respect to the ordered case. The asymptotic expression for the diffusion equation on hyperbolic cellular systems relates random walk on curved lattices to hyperbolic Brownian motion.