Entropic repulsion for massless fields.
type: Item
instance of: scholarly article
title: Entropic repulsion for massless fields.
zbMATH Open document ID: 1045.60103
DOI: 10.1016/S0304-4149(00)00030-2
author: Giambattista Giacomin
author: Jean-Dominique Deuschel
published in: Stochastic Processes and their Applications
publication date: 2004-09-07T00:00:00Z
review text: Random interfaces described in terms of heights \(\{\varphi _x\in \mathbb R;\;x\in \mathbb Z^d\}\) that are zero outside of the sets \(D_N=ND\cap \mathbb Z^d\) for some connected bounded domains \(D\) and large natural numbers \(N\) are investigated. Gibbs probabilities \(P_N\) are given by the massless Hamiltonians of the form \(\sum _{\langle x,y\rangle} V(\varphi _x-\varphi _y)\) with sufficiently smooth convex even \(V\)'s. Various upper and lower bounds are derived for \(\log P_N(\Omega ^+(A_N))\), where \(\Omega ^+(A_N)=\{\varphi ;\;\varphi _x\geq 0\text{ for }x\in A_N\}\) for \(A\subset D\). As corollaries, bounds \[ \limsup _N \sup _{x\in D_N} P_N(\varphi _x>\sqrt {C(\log N)^i}\mid \Omega ^+(D_N))=0 \] and \[ \lim _N \sup _{x\in D_{\delta N}} P_N(\varphi _x<\sqrt {K(\log N)^i}\mid \Omega ^+(D_N))=0 \] describing the entropic repulsion effect are obtained, where \(i=2\) for \(d=2\) and \(i=1\) for \(d>2\).
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82C24
zbMATH DE Number: 2098357
zbMATH Keywords: Gibbs measure
zbMATH Keywords: massless fields
zbMATH Keywords: entropic repulsion
zbMATH Keywords: random surfaces
zbMATH Keywords: random walk in random environment
reviewed by: Petr Holický
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2098357