Concentration inequalities for random fields via coupling

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• 作者：J. -R. Chazottes ; P. Collet ; C. Külske and F. Redig
• 关键词：Exponential concentration ; Stretched ; exponential concentration ; Moment inequality ; Gibbs random fields ; Ising model ; Orlicz space ; Luxembourg norm ; Kantorovich–Rubinstein theorem
• 刊名：Probability Theory and Related Fields
• 出版年：2007
• 出版时间：January, 2007
• 年：2007
• 卷：137
• 期：1-2
• 页码：201-225
• 全文大小：321 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematicsr>Probability Theory and Stochastic Processesr>Mathematical and Computational Physicsr>Quantitative Financer>Mathematical Biologyr>Statistics for Business, Economics, Mathematical Finance and Insurancer>Operation Research and Decision Theoryr>
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-2064

文摘

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.