Stroboscopic exclusion process: a first-moment-driven dynamics

TL;DR

This paper introduces a novel discrete-time exclusion process where jump probabilities depend on the last move, analyzing its density evolution through moment analysis and validating predictions with numerical simulations.

Contribution

It presents a new variant of exclusion processes driven by first-moment dynamics and provides analytical and numerical insights into its behavior.

Findings

Analytical expression for particle density evolution

Excellent agreement between numerical results and theoretical predictions

New model capturing history-dependent jump probabilities

Abstract

We define a new variant of exclusion processes in discrete time that has jump probabilities that depend on the last jump performed. In a particular limit for the jump probabilities and in suitable scaling limits for space and time, we compute the time evolution of the particle density starting from an arbitrary initial configuration, with closed boundary conditions. The core of the argument is the analysis of the time evolution of the moments. Numerical results are compared with the prediction and give excellent agreement.