# Classes of random walks on temporal networks with competing timescales

## TL;DR

This paper explores random walks on stochastic temporal networks with multiple competing timescales, analyzing how these influence behavior, resting times, and the emergence of non-Markovian dynamics, advancing understanding of network processes.

## Contribution

It introduces a general framework for random walks on temporal networks with up to three competing timescales and compares their behaviors and stationary states.

## Key findings

- Mean resting time varies with timescale interactions
- Stationary states depend on network structure and walk model
- Non-Markovian behavior can emerge from memoryless distributions

## Abstract

Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the co-existence of different timescales in the system. Here, we introduce random walks on general stochastic temporal networks allowing for lasting interactions, with up to three competing timescales. We then compare the mean resting time and stationary state of different models. We also discuss the accuracy of the mathematical analysis depending on the random walk model and the structure of the underlying network, and pay particular attention to the emergence of non-Markovian behaviour, even when all dynamical entities are governed by memoryless distributions.