A 0-1 law for the massive Gaussian free field

• 成果类型: Article
• 署名作者: Rodriguez, Pierre-Francois
• 署名单位: University of California System; University of California Los Angeles
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0743-z
• 发表日期: 2017
• 页码: 901-930
• 关键词: strongly correlated systems; random interlacements; PHASE-TRANSITION; fkg inequalities; percolation; sharpness; MODEL; sets

摘要

We investigate the phase transition in a non-planar correlated percolation model with long-range dependence, obtained by considering level sets of a Gaussian free field with mass above a given height h. The dependence present in the model is a notorious impediment when trying to analyze the behavior near criticality. Alongside the critical threshold for percolation, a second parameter characterizes a strongly subcritical regime. We prove that the relevant crossing probabilities converge to 1 polynomially fast below , which (firmly) suggests that the phase transition is sharp. A key tool is the derivation of a suitable differential inequality for the free field that enables the use of a (conditional) influence theorem.