Anomalous diffusion on random graphs

TL;DR

This paper demonstrates that random walks on random graphs with arbitrary degree distributions can exhibit anomalous diffusion due to correlated steps, providing a new algorithm to analyze such behavior and revealing predictable properties distinct from continuous systems.

Contribution

The authors introduce an algorithm to count all possible paths of particles diffusing on random graphs, enabling analysis of anomalous diffusion with arbitrary degree distributions.

Findings

Random walks on random graphs can show anomalous diffusion.

The algorithm accurately calculates mean square displacement.

Anomalous behavior is predictable and differs from continuum models.

Abstract

We show that anomalous diffusion can result when the steps of a random walk are not statistically independent. We present an algorithm that counts all the possible paths of particles diffusing on random graphs with arbitrary degree distribution. Using this to calculate the mean square displacement, we show that in sharp contrast to continua, random walks on random graphs can exhibit anomalous behavior and yet have well-defined and predictable properties.