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Entropic repulsion for a class of Gaussian interface models in high dimensions


Kurt, N (2007). Entropic repulsion for a class of Gaussian interface models in high dimensions. Stochastic Processes and their Applications, 117(1):23-34.

Abstract

Consider the centred Gaussian field on the lattice View the MathML source, d large enough, with covariances given by the inverse of View the MathML source, where Δ is the discrete Laplacian and View the MathML source, the qj satisfying certain additional conditions. We extend a previously known result to show that the probability that all spins are nonnegative on a box of side-length N has an exponential decay at a rate of order Nd−2klogN. The constant is given in terms of a higher-order capacity of the unit cube, analogously to the known case of the lattice free field. This result then allows us to show that, if we condition the field to stay positive in the N-box, the local sample mean of the field is pushed to a height of order View the MathML source.

Abstract

Consider the centred Gaussian field on the lattice View the MathML source, d large enough, with covariances given by the inverse of View the MathML source, where Δ is the discrete Laplacian and View the MathML source, the qj satisfying certain additional conditions. We extend a previously known result to show that the probability that all spins are nonnegative on a box of side-length N has an exponential decay at a rate of order Nd−2klogN. The constant is given in terms of a higher-order capacity of the unit cube, analogously to the known case of the lattice free field. This result then allows us to show that, if we condition the field to stay positive in the N-box, the local sample mean of the field is pushed to a height of order View the MathML source.

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8 citations in Web of Science®
8 citations in Scopus®
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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
Language:English
Date:2007
Deposited On:04 Nov 2009 15:36
Last Modified:05 Apr 2016 13:23
Publisher:Elsevier
ISSN:0304-4149
Publisher DOI:https://doi.org/10.1016/j.spa.2006.05.011
Related URLs:http://arxiv.org/abs/math/0510143v3
http://www.ams.org/mathscinet-getitem?mr=2287101

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