ON THE RADIUS OF GAUSSIAN FREE FIELD EXCURSION CLUSTERS

• 成果类型: Article
• 署名作者: Goswami, Subhajit; Rodriguez, Pierre-Francois; Severo, Franco
• 署名单位: Tata Institute of Fundamental Research (TIFR); Imperial College London; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1569
• 发表日期: 2022
• 页码: 1675-1724
• 关键词: entropic repulsion; correlation length; critical-behavior; PHASE-TRANSITION; percolation

摘要

We consider the Gaussian free field phi on Z(d), for d >= 3, and give sharp bounds on the probability that the radius of a finite cluster in the excursion set {phi >= h} exceeds a large value N for any height h not equal h(*), where h(*) refers to the corresponding percolation critical parameter. In dimension 3, we prove that this probability is subexponential in N and decays as exp{-pi/6 (h - h(*))(2) N/logN} as N -> infinity to principal exponential order. When d >= 4, we prove that these tails decay exponentially in N. Our results extend to other quantities of interest, such as truncated two-point functions and the two-arms probability for annuli crossings at scale N.