Non-monotonic displacement distribution of active random walkers

TL;DR

This paper analyzes a model of active random walkers with temporal correlations, revealing conditions under which their displacement distribution becomes non-monotonic, influenced by forward movement tendency and correlation strength.

Contribution

It introduces an analytical and numerical study of non-monotonic displacement distributions in active random walks with general temporal correlations.

Findings

Non-monotonic displacement distribution occurs under certain conditions.

Strong persistence is necessary for non-monotonicity in homogeneous systems.

Correlations influence the shape and magnitude of the distribution.

Abstract

We consider a simple model for active random walk with general temporal correlations, and investigate the shape of the probability distribution function of the displacement during a short time interval. We find that under certain conditions the distribution is non-monotonic and we show analytically and numerically that the existence of the non-monotonicity is governed by the walker's tendency to move forward, while the correlations between the timing of its active motion control the magnitude and shape of the non-monotonicity. In particular, we find that in a homogeneous system such non-monotonicity can occur only if the persistence is strong enough.