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Entropic repulsion of the lattice free field


Bolthausen, E; Deuschel, J-D; Zeitouni, O (1995). Entropic repulsion of the lattice free field. Communications in Mathematical Physics, 170(2):417-443.

Abstract

Consider the massless free field on the d-dimensional lattice ℤ d , d≥3; that is the centered Gaussian field on ℝ ℤ d with covariances given by the Green function of the simple random walk on ℤ d . We show that the probability, that all the spins are positive in a box of volume N d , decays exponentially at a rate of order N d-2 logN and compute explicitly the corresponding constant in terms of the capacity of the unit cube. The result is extended to a class of transient random walks with transition functions in the domain of the normal and α-stable law.

Abstract

Consider the massless free field on the d-dimensional lattice ℤ d , d≥3; that is the centered Gaussian field on ℝ ℤ d with covariances given by the Green function of the simple random walk on ℤ d . We show that the probability, that all the spins are positive in a box of volume N d , decays exponentially at a rate of order N d-2 logN and compute explicitly the corresponding constant in terms of the capacity of the unit cube. The result is extended to a class of transient random walks with transition functions in the domain of the normal and α-stable law.

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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; Green function; random walk
Language:English
Date:1995
Deposited On:27 Apr 2010 14:08
Last Modified:06 Dec 2017 21:05
Publisher:Springer
ISSN:0010-3616
Additional Information:The original publication is available at www.springerlink.com
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/BF02108336
Related URLs:http://projecteuclid.org/euclid.cmp/1104273128 (Organisation)
http://www.zentralblatt-math.org/NEW/zmath/search/?q=an%3A0821.60040
http://www.ams.org/mathscinet-getitem?mr=1334403
https://www.zora.uzh.ch/22069

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