NONLINEAR LARGE DEVIATIONS: BEYOND THE HYPERCUBE

• 成果类型: Article
• 署名作者: Yan, Jun
• 署名单位: Stanford University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1516
• 发表日期: 2020
• 页码: 812-846
• 关键词: upper tails

摘要

By extending (Adv. Math. 299 (2016) 396-450), we present a framework to calculate large deviations for nonlinear functions of independent random variables supported on compact sets in Banach spaces. Previous research on nonlinear large deviations has only focused on random variables supported on {-1, +1}(n), and accordingly we build theory for random variables with general distributions, increasing flexibility in the applications. As examples, we compute the large deviation rate functions for monochromatic subgraph counts in edge-colored complete graphs, and for triangle counts in dense random graphs with continuous edge weights. Moreover, we verify the mean field approximation for a class of vector spin models.