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Scaling Limits of Interacting Particle Systems pp 287–310Cite as

Equilibrium Fluctuations of Reversible Dynamics

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

Abstract

In Chapters 4 to 7 we examined the hydrodynamic behavior of several mean-zero interacting particle systems and proved a law of large numbers under diffusive resealing for the empirical measure. We now investigate the fluctuations of the empirical measure around the hydrodynamic limit starting from an equilibrium state. To fix ideas, we consider the nearest neighbor symmetric zero range process. The reader shall notice, however, that the approach presented below applies to a large class of reversible models including nongradient systems. The generator of this process is

$$\left( {{L_N}f} \right)\left( \eta \right) = \sum\limits_{x,y \in {\Bbb T}_N^d} {p\left( y \right)g\left( {\eta \left( x \right)} \right)\left[ {f\left( {{\eta ^{x,x + y}}} \right) - f\left( \eta \right)} \right]} ,$$
(0.1)

where p(y) = 1/2 if |y| = 1 and 0 otherwise and g is a rate function satisfying the assumptions of Definition 2.3.1.

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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). Equilibrium Fluctuations of Reversible Dynamics. 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_12

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  • DOI: https://doi.org/10.1007/978-3-662-03752-2_12

  • 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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