International audienceWe derive by a constructive method the hydrodynamic behavior of attractive processes with irreducible jumps and product invariant measures. Our approach relies on (i) explicit construction of Riemann solutions without assuming convexity, which may lead to contact discontinuities and (ii) a general result which proves that the hydrodynamic limit for Riemann initial profiles implies the same for general initial pro5les. The k-step exclusion process provides a simple example. We also give a law of large numbers for the tagged particle in a nearest neighbor asymmetric k-step exclusion process

We prove almost sure Euler hydrodynamics for a large class of attractive particle systems on Z starting from an arbitrary initial profile. We generalize earlier works by Seppäläinen (1999) and Andjel et al. (2004). Our constructive approach requires new ideas since the subadditive ergodic theorem (central to previous works) is no longer effective in our setting. 0 AMS 2000 subject classification. Primary 60K35; Secondary 82C22.

We consider attractive irreducible conservative particle systems on $\mathbb{Z}$, without necessarily nearest-neighbor jumps or explicit invariant measures. We prove that for such systems, the hydrodynamic limit under Euler time scaling exists and is given by the entropy solution to some scalar conservation law with Lipschitz-continuous flux. Our approach is a generalization of Bahadoran et al. [Stochastic Process. Appl. 99 (2002) 1--30], from which we relax the assumption that the process has explicit invariant measures.Comment: Published at http://dx.doi.org/10.1214/009117906000000115 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

We consider attractive particle systems in Z d with product invariant measures. We prove that when particles are restricted to a subset of Z d , with birth and death dynamics at the boundaries, the hydrodynamic limit is given by the unique entropy solution of a conservation law, with boundary conditions in the sense of Bardos et al. ([7]). For the hydrostatic limit between parallel hyperplanes, we prove a multidimensional version of the phase diagram conjectured in [38], and show that it is robust with respect to perturbations of the boundaries.AMS 2000 subject classifications. 60K35, 82C22, 82C26; 35L65, 35L67, 35L50.

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.