Exclusion type spatially heterogeneous processes in continuum

TL;DR

This paper rigorously analyzes deterministic exclusion processes in continuum with spatial heterogeneity, focusing on ergodic averages and their relation to densities, using a novel dynamical coupling method as a diagnostic tool.

Contribution

It introduces a new dynamical coupling approach to study heterogeneous exclusion processes and establishes connections between ergodic velocities and densities.

Findings

Ergodic particle velocities are characterized in heterogeneous environments.

Connections between velocities and densities are rigorously established.

The dynamical coupling method provides new insights into process diagnostics.

Abstract

We study deterministic discrete time exclusion type spatially heterogeneous particle processes in continuum. A typical example of this sort is a traffic flow model with obstacles: traffic lights, speed bumps, spatially varying local velocities etc. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to particle and obstacles densities (the so called Fundamental Diagram) is analyzed rigorously. The main technical tool is a "dynamical" coupling construction applied in a nonstandard fashion: instead of proving the existence of the successful coupling (which even might not hold) we use its presence/absence as an important diagnostic tool.