# Modeling random walkers on growing random networks

## TL;DR

This paper develops continuum models to describe how a random walker's position evolves on growing networks under various growth algorithms, providing accurate approximations for quasi-stationary regimes.

## Contribution

It introduces new continuum models for random walkers on growing networks, including methods to approximate pair probabilities in quasi-stationary states.

## Key findings

- Models accurately describe walker position evolution.
- Approximate solutions enable tractable analysis.
- Applicable to networks with different growth algorithms.

## Abstract

We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the random walker controls the network topology. For motility rates in which the position of the walker can be treated as quasi-stationary, we present accurate approximations to replace pair probabilities that allow us to numerically solve an otherwise intractable system of equations.