Exclusion-type spatially heterogeneous processes in continua

We study deterministic discrete time exclusion-type spatially heterogeneous particle processes in continua. 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 obstacle densities (the so-called fundamental diagram), are 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 might even fail to hold) we use its presence/absence as an important diagnostic tool.