Stationary currents in particle systems with constrained hopping rates

TL;DR

This paper investigates how constraints on hopping rates in stochastic particle systems, specifically Zero Range Processes, affect stationary currents, providing explicit formulas and relevance to pedestrian movement modeling.

Contribution

It introduces exact formulas for stationary currents in constrained Zero Range Processes, linking theoretical results to pedestrian dynamics applications.

Findings

Constraints reduce stationary currents

Explicit formulas derived for specific cases

Relevance to pedestrian movement modeling

Abstract

We study the effect on the stationary currents of constraints affecting the hopping rates in stochastic particle systems. In the framework of Zero Range Processes with drift within a finite volume, we discuss how the current is reduced by the presence of the constraint and deduce exact formulae, fully explicit in some cases. The model discussed here has been introduced in Ref. [1] and is relevant for the description of pedestrian motion in elongated dark corridors, where the constraint on the hopping rates can be related to limitations on the interaction distance among pedestrians.