On the probability of staying above a wall for the -dimensional SOS model at low temperature

• 成果类型: Article
• 署名作者: Caputo, Pietro; Martinelli, Fabio; Toninelli, Fabio Lucio
• 署名单位: Roma Tre University; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0658-0
• 发表日期: 2015
• 页码: 803-831
• 关键词: lattice free-field; entropic repulsion; interface; SURFACES

摘要

We obtain sharp asymptotics for the probability that the -dimensional discrete SOS interface at low temperature is positive in a large region. For a square region , both under the infinite volume measure and under the measure with zero boundary conditions around , this probability turns out to behave like , with the surface tension at zero tilt, also called step free energy, and L the box side. This behavior is qualitatively different from the one found for continuous height massless gradient interface models (Bolthausen et al., Commun Math Phys 170(2):417-443, 1995; Deuschel et al., Stochastic Process Appl 89(2):333-354, 2000).