Large Deviations andVariational Principle for Harmonic Crystals
Abstract
We consider massless Gaussian fields with covariance related to the Green function of a long range random walk on ^{d}. These are viewed as Gibbs measures for a linearquadratic interaction. 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2000
 Bibcode:
 2000CMaPh.209..595C