Strict inequalities for arm exponents in planar percolation

• 成果类型: Article
• 署名作者: Radhakrishnan, Ritvik Ramanan; Tassion, Vincent
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-025-01448-8
• 发表日期: 2026-06
• 页码: 659-688
• 关键词: sensitivity

摘要

We discuss a general method to obtain quantitative improvements of correlation inequalities and apply it to arm estimates for Bernoulli bond percolation on Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Z}}<^>2$$\end{document}. Our first result is that the two-arm exponent is strictly larger than twice the one-arm exponent and can be seen as a quantitative improvement of the Harris-FKG inequality. This answers a question of Garban and Steif [10, Open Problem 13.6], which was motivated by the study of exceptional times in dynamical percolation [24, section 9]. Our second result is that the monochromatic arm exponents are strictly larger than their polychromatic versions, and can be seen as a quantitative improvement of Reimer's main lemma [1, Lemma 4.1]. This second result is not new; it was already proved by Beffara and Nolin [3] using a different argument.