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Critical Large Deviations for Gaussian Fields in the Phase Transition Regime, I

Erwin Bolthausen and Jean-Dominique Deuschel
The Annals of Probability
Vol. 21, No. 4 (Oct., 1993), pp. 1876-1920
Stable URL: http://www.jstor.org/stable/2244703
Page Count: 45
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Critical Large Deviations for Gaussian Fields in the Phase Transition Regime, I
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Abstract

We investigate large deviations for the empirical distribution functional of a Gaussian random field on RZd , d ≥ 3, in the phase transition regime. We first prove that the specific entropy governs an Nd volume order large deviation principle outside the Gibbsian class. Within the Gibbsian class we derive an Nd-2 capacity order large deviation principle with exact rate function, and we apply this result to the asymptotics of microcanonical ensembles. We also give a spins' profile description of the field and show that smooth profiles obey Nd-2 order large deviations, whereas discontinuous profiles obey Nd-1 surface order large deviations.

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