Exclusion type spatially heterogeneous processes in continuum

Details Exclusion type spatially heterogeneous processes in continuum Exclusion type spatially heterogeneous processes in continuum

2011-05-21

arxiv.org/abs/1105.4232v2

Mathematics

Dynamical Systems

17 pages, minor corrections, accepted for publication in JSTAT

Scientific paper

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.

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