Concentration inequalities for random fields via coupling

• 成果类型: Article
• 署名作者: Chazottes, J. R.; Collet, P.; Kuelske, C.; Redig, F.
• 署名单位: Leiden University; Leiden University - Excl LUMC; University of Groningen; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0026-1
• 发表日期: 2007
• 页码: 201-225
• 关键词: percolation

摘要

We present a new and simple approach to concentration inequalities in the context of dependent random processes and random fields. Our method is based on coupling and does not use information inequalities. In case one has a uniform control on the coupling, one obtains exponential concentration inequalities. If such a uniform control is no more possible, then one obtains polynomial or stretched-exponential concentration inequalities. Our abstract results apply to Gibbs random fields, both at high and low temperatures and in particular to the low-temperature Ising model which is a concrete example of non-uniformity of the coupling.