- 99-162 P. Caputo, J.D. Deuschel
- Large deviations and variational principle for harmonic crystals
May 11, 99
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Abstract. We consider massless
Gaussian fields with covariance
related to the Green function of a long range random walk on $\bbZ^d$.
These are viewed as Gibbs measures for a
We establish thermodynamic identities and prove a
version of Gibbs' variational principle, showing that
translation invariant Gibbs measures are characterized as
minimizers of the relative entropy density.
We then study the large deviations of the empirical field
of a Gibbs measure. We show that a weak
large deviation principle holds at the volume order,
with rate given by the relative entropy density.