The universal relation between scaling exponents in first-passage percolation

• 成果类型: Article
• 署名作者: Chatterjee, Sourav
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.177.2.7
• 发表日期: 2013
• 页码: 663-697
• 关键词: 1st passage percolation; ballistic deposition; directed polymers; GROWTH; shape; fluctuations; interface

摘要

It has been conjectured in numerous physics papers that in ordinary first-passage percolation on integer lattices, the fluctuation exponent chi and the wandering exponent are related through the universal relation chi = 2 xi - 1, irrespective of the dimension. This is sometimes called the KPZ relation between the two exponents. This article gives a rigorous proof of this conjecture assuming that the exponents exist in a certain sense.