Abstract:
We consider massless Gaussian fields with covariance related to the Green function of a long range random walk on ℤd. These are viewed as Gibbs measures for a linear-quadratic 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.
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Received: 2 June 1999 / Accepted: 9 August 1999
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Caputo, P., Deuschel, JD. Large Deviations and¶Variational Principle for Harmonic Crystals. Comm Math Phys 209, 595–632 (2000). https://doi.org/10.1007/PL00020962
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DOI: https://doi.org/10.1007/PL00020962