Equilibrium Fluctuations

  • Herbert Spohn
Part of the Texts and Monographs in Physics book series (TMP)


We want to understand the dynamics of the hard core lattice gas in 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
$$ \left\langle {{{\eta }_{t}}\left( x \right)} \right\rangle = \rho $$
for every t, x. Conditions 1.1, 1.2, 1.5, 1.6, and 1.7 (i) are assumed throughout.


Density Fluctuation Gibbs Measure Detailed Balance Equilibrium Measure Scaling Limit 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Herbert Spohn
    • 1
  1. 1.Theoretische PhysikLudwig-Maximilians-Universität MünchenMünchen 2Fed. Rep. of Germany

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