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Hydrodynamic Limit of Reversible Nongradient Systems

  • Claude Kipnis
  • Claudio Landim
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 320)

Abstract

We investigate in this chapter the hydrodynamic behavior of reversible nongradient systems. To fix ideas we consider one of the simplest examples, the so called symmetric generalized exclusion process. This is the Markov process introduced in section 2.4 that describes the evolution of particles on a lattice with an exclusion rule that allows at most k particles per site. Here K is a fixed positive integer greater or equal than 2. The generator of this Markov process acts on cylinder functions as
$$\left( {{L_N}f} \right)\left( \eta \right) = \left( {1/2} \right)\sum\limits_{\mathop {x,y \in {T^d}}\limits_{|x - y| = 1} } {r\left( {\eta \left( x \right),\eta \left( y \right)} \right)} \left[ {f\left( {{\eta ^{x,y}}} \right) - f\left( \eta \right)} \right],$$
(0.1)
where r(a, b) = 1{a > 0, b < k} and η x, y is the configuration obtained from η moving a particle from x to y.

Keywords

Dirichlet Form Variational Formula Exclusion Process Hydrodynamic Limit Hydrodynamic Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Claude Kipnis
    • 1
    • 2
  • Claudio Landim
    • 1
    • 2
  1. 1.Instituto de Matematica Pura e AplicadaRio de JaneiroBrasil
  2. 2.CNRS UPRES-A 6085Université de RouenMont Saint Aignan CedexFrance

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