Liouville metric of star-scale invariant fields: tails and Weyl scaling

• 成果类型: Article
• 署名作者: Dubedat, Julien; Falconet, Hugo
• 署名单位: Columbia University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-019-00919-z
• 发表日期: 2020
• 页码: 293-352
• 关键词: percolation; LIMITS

摘要

We study the Liouville metric associated to an approximation of a log-correlated Gaussian field with short range correlation. We show that below a parameter gamma(c) > 0, the left-right length of rectangles for the Riemannian metric e(gamma phi 0,n)ds(2) with various aspect ratio is concentrated with quasi-lognormal tails, that the renormalized metric is tight when gamma < min(gamma(c), 0.4) and that subsequential limits are consistent with the Weyl scaling.