Large Scale Dynamics of Interacting Particles pp 175-211 | Cite as

# Equilibrium Fluctuations

Chapter

## Abstract

We want to understand the dynamics of the hard core lattice gas in
for every

*thermal equilibrium*. The initial (*t*= 0) measure is then the Gibbs measure < · >_{ ρ }for the potential {*J*_{ A }, |*A*| ≧ 2} and with average density*ρ*, 0 ≦*ρ*≦ 1. By time stationarity the process*η*_{ t }can be extended to*t*≦ O. Therefore*η*_{ t }(x), t∈ℝ, x∈ℤ^{ d }, is a reversible process stationary in space and time. Without risk of confusion space-time averages for*η*_{ t }(x) will also be denoted by < · >_{ ρ }. The average density*ρ*will be fixed throughout and we will omit the subscript*ρ*. The distribution of {*η*_{ t }(x), x∈ℤ^{ d }at a single time is the equilibrium measure < · >, in particular$$ \left\langle {{{\eta }_{t}}\left( x \right)} \right\rangle = \rho $$

(2.1)

*t*,*x*. Conditions 1.1, 1.2, 1.5, 1.6, and 1.7 (i) are assumed throughout.## Keywords

Density Fluctuation Gibbs Measure Detailed Balance Equilibrium Measure Scaling Limit
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.

## Preview

Unable to display preview. Download preview PDF.

## Copyright information

© Springer-Verlag Berlin Heidelberg 1991