Blog
About

9
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Coupling, Attractiveness and Hydrodynamics for Conservative Particle Systems

      Preprint

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          Attractiveness is a fundamental tool to study interacting particle systems and the basic coupling construction is a usual route to prove this property, as for instance in simple exclusion. The derived Markovian coupled process \((\xi_t,\zeta_t)_{t\geq 0}\) satisfies: (A) if \(\xi_0\leq\zeta_0\) (coordinate-wise), then for all \(t\geq 0\), \(\xi_t\leq\zeta_t\) a.s. In this paper, we consider generalized misanthrope models which are conservative particle systems on \(\Z^d\) such that, in each transition, \(k\) particles may jump from a site \(x\) to another site \(y\), with \(k\geq 1\). These models include simple exclusion for which \(k=1\), but, beyond that value, the basic coupling construction is not possible and a more refined one is required. We give necessary and sufficient conditions on the rates to insure attractiveness; we construct a Markovian coupled process which both satisfies (A) and makes discrepancies between its two marginals non-increasing. We determine the extremal invariant and translation invariant probability measures under general irreducibility conditions. We apply our results to examples including a two-species asymmetric exclusion process with charge conservation (for which \(k\le 2\)) which arises from a Solid-on-Solid interface dynamics, and a stick process (for which \(k\) is unbounded) in correspondence with a generalized discrete Hammersley-Aldous-Diaconis model. We derive the hydrodynamic limit of these two one-dimensional models.

          Related collections

          Most cited references 5

          • Record: found
          • Abstract: not found
          • Book: not found

          Scaling Limits of Interacting Particle Systems

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Stochastic Inequalities on Partially Ordered Spaces

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Processus des misanthropes

                Bookmark

                Author and article information

                Journal
                10.1214/09-AIHP347
                0903.0316

                Mathematical physics, Mathematical & Computational physics, Probability

                Comments

                Comment on this article