Residence time of symmetric random walkers in a strip with large reflective obstacles

TL;DR

This paper investigates how large obstacles affect the residence time of symmetric random walkers in a 2D strip, revealing non-monotonic behavior and providing an exact 1D analog for analysis.

Contribution

It introduces a 1D model with defect sites that accurately predicts the residence time behavior observed in the 2D system, including exact calculations.

Findings

Residence time varies non-monotonically with obstacle size and position.

Presence of obstacles can reduce the average crossing time.

The 1D defect model matches Monte Carlo simulations perfectly.

Abstract

We study the effect of a large obstacle on the so called residence time, i.e., the time that a particle performing a symmetric random walk in a rectangular (2D) domain needs to cross the strip. We observe a complex behavior, that is we find out that the residence time does not depend monotonically on the geometric properties of the obstacle, such as its width, length, and position. In some cases, due to the presence of the obstacle, the mean residence time is shorter with respect to the one measured for the obstacle--free strip. We explain the residence time behavior by developing a 1D analog of the 2D model where the role of the obstacle is played by two defect sites having a smaller probability to be crossed with respect to all the other regular sites. The 1D and 2D models behave similarly, but in the 1D case we are able to compute exactly the residence time finding a perfect match with the Monte Carlo simulations.