NONLINEAR LARGE DEVIATION BOUNDS WITH APPLICATIONS TO WIGNER MATRICES AND SPARSE ERDOS-RENYI GRAPHS

• 成果类型: Article
• 署名作者: Augeri, Fanny
• 署名单位: Weizmann Institute of Science
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1427
• 发表日期: 2020
• 页码: 2404-2448
• 关键词: upper tails; Mean-field; complexity; number

摘要

We prove general nonlinear large deviation estimates similar to Chatterjee-Dembo's original bounds, except that we do not require any second order smoothness. Our approach relies on convex analysis arguments and is valid for a broad class of distributions. Our results are then applied in three different setups. Our first application consists in the mean-field approximation of the partition function of the Ising model under an optimal assumption on the spectra of the adjacency matrices of the sequence of graphs. Next, we apply our general large deviation bound to investigate the large deviation of the traces of powers of Wigner matrices with sub-Gaussian entries and the upper tail of cycles counts in sparse Erdos-Renyi graphs down to the sparsity threshold n(-1/2).