A SIMPLIFIED PROOF OF THE RELATION BETWEEN SCALING EXPONENTS IN FIRST-PASSAGE PERCOLATION

• 成果类型: Article
• 署名作者: Auffinger, Antonio; Damron, Michael
• 署名单位: University of Chicago; Princeton University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP854
• 发表日期: 2014
• 页码: 1197-1211
• 关键词: passage percolation; fluctuations; shape

摘要

In a recent breakthrough work, Chatterjee [Ann. of Math. (2) 177 (2013) 663-697] proved a long standing conjecture that relates the transversal exponent and the fluctuation exponent x in first-passage percolation on Z(d). The purpose of this paper is to replace the main argument of Chatterjee (2013) and give an alternative proof of this relation. Specifically, we show that under the assumption that exponents defined in Chatterjee (2013) exist, one has the relation x <= 2 xi - 1. One advantage of our argument is that it does not require the nearly Gamma assumption of Chatterjee (2013).