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Article

Exclusion type spatially heterogeneous processes in continuum

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.