On exclusion type inhomogeneous interacting particle systems

Abstract

For a large class of inhomogeneous interacting particle systems (IPS) on a lattice we develop a rigorous method for mapping them onto homogeneous IPS. Our novel approach provides a direct way of obtaining the statistical properties of such inhomogeneous systems by studying the far simpler homogeneous systems. In the cases when the latter can be solved exactly our method yields an exact solution for the statistical properties of an inhomogeneous IPS. This approach is illustrated by studies of three of IPS, namely those with particles of different sizes, or with varying (between particles) maximal velocities, or accelerations.