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Critical large deviations for Gaussian fields in the phase transition regime. I


Bolthausen, E; Deuschel, J-D (1993). Critical large deviations for Gaussian fields in the phase transition regime. I. The Annals of Probability, 21(4):1876-1920.

Abstract

We investigate large deviations for the empirical distribution functional of a Gaussian random field on $\mathbb{R}^{\mathbb{Z}^d}, d \geq 3$, in the phase transition regime. We first prove that the specific entropy governs an $N^d$ volume order large deviation principle outside the Gibbsian class. Within the Gibbsian class we derive an $N^{d-2}$ 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 $N^{d-2}$ order large deviations, whereas discontinuous profiles obey $N^{d-1}$ surface order large deviations.

We investigate large deviations for the empirical distribution functional of a Gaussian random field on $\mathbb{R}^{\mathbb{Z}^d}, d \geq 3$, in the phase transition regime. We first prove that the specific entropy governs an $N^d$ volume order large deviation principle outside the Gibbsian class. Within the Gibbsian class we derive an $N^{d-2}$ 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 $N^{d-2}$ order large deviations, whereas discontinuous profiles obey $N^{d-1}$ surface order large deviations.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Large deviations; random fields; Gaussian processes; statistical mechanics
Language:English
Date:1993
Deposited On:20 May 2010 15:25
Last Modified:05 Apr 2016 13:28
Publisher:Institute of Mathematical Statistics
ISSN:0091-1798
Publisher DOI:10.1214/aop/1176989003
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1245293
http://www.zentralblatt-math.org/zmath/en/search/?q=an:0801.60018
Permanent URL: http://doi.org/10.5167/uzh-22672

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