1. Wall repulsion and mutual interface repulsion: a harmonic crystal model in high dimensions
- Author
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Giambattista Giacomin, Daniela Bertacchi, Bertacchi, D, Giacomin, G, Benassù, Serena, Laboratoire de Probabilités et Modèles Aléatoires (LPMA), and Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Statistics and Probability ,[MATH.MATH-PR] Mathematics [math]/Probability [math.PR] ,large deviation ,Monotonic function ,Geometry ,01 natural sciences ,harmonic crystal ,010104 statistics & probability ,entropic repulsion ,Lattice (order) ,Crystal model ,Modelling and Simulation ,Statistical physics ,0101 mathematics ,extrema of random field ,Mathematics ,Gaussian field ,Random field ,Stochastic process ,Applied Mathematics ,Extrema of random fields ,010102 general mathematics ,random walks ,Random walk ,Gaussian fields ,Multi–interface phenomena ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,Large deviations ,MAT/06 - PROBABILITA E STATISTICA MATEMATICA ,Modeling and Simulation ,Probability distribution ,multi-interface phenomena ,Large deviations theory - Abstract
We consider two independent lattice harmonic crystals in dimension d greater than or equal to 3 constrained to live in the upper half-plane and to lie one above the other in a large region. We identify the leading order asymptotics of this model, both from the point of view of probability estimates and of pathwise behavior: this gives a rather complete picture of the phenomenon via a detailed analysis of the underlying entropy-energy competition. From the technical viewpoint, with respect to earlier work on sharp constants for harmonic entropic repulsion, this model is lacking certain monotonicity properties and the main tool that allows to overcome this difficulty is the comparison with suitable rough substrate models. (C) 2003 Elsevier B.V. All rights reserved.
- Published
- 2004