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Scaling Limits of Interacting Particle Systems pp 67–114Cite as

An Example of Reversible Gradient System: Symmetric Zero Range Processes

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Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 320))

Abstract

In this chapter we investigate the hydrodynamic behavior of reversible gradient interacting particle systems. To keep notation simple and to avoid minor technical difficulties, we consider the simplest prototype of reversible gradient system: the nearest neighbor symmetric zero range process. The generator of this Markov process is given by

$$({L_N}f)(\eta ) = (1/2)\mathop \Sigma \limits_{x \in T_N^d} \sum\limits_{|z| = 1} {g(\eta (x))} [f({\eta ^{x,x + z}}) - f(\eta )]$$
(0.1)

for cylinder functions f: ℕT dN →ℝ.

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Authors and Affiliations

  1. Instituto de Matematica Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brasil

    Claude Kipnis & Claudio Landim

  2. CNRS UPRES-A 6085, Université de Rouen, F-76128, Mont Saint Aignan Cedex, France

    Claude Kipnis & Claudio Landim

Authors
  1. Claude Kipnis
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  2. Claudio Landim
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© 1999 Springer-Verlag Berlin Heidelberg

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Kipnis, C., Landim, C. (1999). An Example of Reversible Gradient System: Symmetric Zero Range Processes. In: Scaling Limits of Interacting Particle Systems. Grundlehren der mathematischen Wissenschaften, vol 320. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03752-2_6

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  • DOI: https://doi.org/10.1007/978-3-662-03752-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08444-7

  • Online ISBN: 978-3-662-03752-2

  • eBook Packages: Springer Book Archive

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