Biased random walk on random networks in presence of stochastic resetting: Exact results

TL;DR

This paper provides exact results for biased random walks on disordered comb networks, analyzing how stochastic resetting influences stationary states and drift velocities, revealing conditions for non-zero drift and the impact of resetting on trapping.

Contribution

It introduces exact analytical solutions for biased random walks with stochastic resetting on disordered comb networks, highlighting how resetting affects drift and trapping phenomena.

Findings

Resetting enables escape from trapping at long branches.

Non-zero drift velocity depends on bias and resetting.

Resetting maintains finite drift velocity at all biases.

Abstract

We consider biased random walks on random networks constituted by a random comb comprising a backbone with quenched-disordered random-length branches. The backbone and the branches run in the direction of the bias. For the bare model as also when the model is subject to stochastic resetting, whereby the walkers on the branches reset with a constant rate to the respective backbone sites, we obtain exact stationary-state static and dynamic properties for a given disorder realization of branch lengths sampled following an arbitrary distribution. We derive a criterion to observe in the stationary state a non-zero drift velocity along the backbone. For the bare model, we discuss the occurrence of a drift velocity that is non-monotonic as a function of the bias, becoming zero beyond a threshold bias because of walkers trapped at very long branches. Further, we show that resetting allows the system to escape trapping, resulting in a drift velocity that is finite at any bias.