We consider finite-range, nonzero mean, one-dimensional exclusion processes on Z. We show that, if the initial configuration has "density" α, then the process converges in distribution to the product Bernoulli measure with mean density α. From this we deduce the strong form of local equilibrium in the hydrodynamic limit for non-product initial measures.
We extend the strong macroscopic stability introduced in Bramson & Mountford
(2002) for one-dimensional asymmetric exclusion processes with finite range to
a large class of one-dimensional conservative attractive models (including
misanthrope process) for which we relax the requirement of finite range
kernels. A key motivation is extension of constructive hydrodynamics result of
Bahadoran et al. (2002, 2006, 2008) to nonfinite range kernels
We prove, using results for hydrodynamic limits, that an exclusion process starting from an ergodic initial distribution converges to product measure in one dimension. Our only assumption is the existence of a nonzero mean for the underlying random walk.
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