APPLICATIONS OF STEIN'S METHOD FOR CONCENTRATION INEQUALITIES

• 成果类型: Article
• 署名作者: Chatterjee, Sourav; Dey, Partha S.
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP542
• 发表日期: 2010
• 页码: 2443-2485
• 关键词: sums; deviations; statistics; number

摘要

Stein's method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the theory and three applications: (1) We obtain a concentration inequality for the magnetization in the Curie-Weiss model at critical temperature (where it obeys a nonstandard normalization and super-Gaussian concentration). (2) We derive exact large deviation asymptotics for the number of triangles in the Erdos-Renyi random graph G(n, p) when p >= 0.31. Similar results are derived also for general subgraph counts. (3) We obtain some interesting concentration inequalities for the Ising model on lattices that hold at all temperatures.