Shocks in one-dimensional processes with drift

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This paper has appeared in Probability and Phase Transition, edited by Geoffrey Grimmett, NATO SCIENCE SERIES: C: Mathematical and Physical Sciences Volume 420, Kluwer

P.A. Ferrari


The local structure of shocks in one dimensional, nearest neighbor attractive systems with drift and conserved density is reviewed. The systems include the asymmetric simple exclusion, the zero range and the ``misanthropes'' processes. The microscopic shock is identified by a ``second class particle'' initially located at the origin. Second class particles also describe the behavior of the characteristics of the macroscopic equation related to the corresponding model when the hydrodynamic limit is performed. Law of large numbers and central limit theorems as well as the convergence of the system at the average position of the shock are reviewed.


Last modified: Thu Jan 21 15:46:10 BRST 2010