Residence time in one-dimensional random walks in presence of moving defects

Abstract

Residence time is relevant in several applicative problems, such as the pedestrian motion in presence of queues and the study of water flows in runoff ponds. In this last context, it is important to control the residence time since it is strictly connected to the pond efficiency in terms of deposition of pollutants. These applications motivated our detailed study of residence time in presence of moving obstacles and defects for a particle performing a one-dimensional random walk. More precisely, for a particle conditioned to exit through the right endpoint, we measure the typical time needed to cross the entire lattice in presence of defects. These are defined as lattice sites with jump probabilities modified adding a bias to the values used at regular sites. We find explicit formulae for the residence time and discuss several models of moving defects. The presence of a stochastic updating rule for the motion of the defect smooths the local residence time profiles found in the case of a static defect.