Estimation in spin glasses: A first step

• 成果类型: Article
• 署名作者: Chatterjee, Sourav
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000109
• 发表日期: 2007
• 页码: 1931-1946
• 关键词: sherrington-kirkpatrick model; RANDOM MATRICES; systems; lattice

摘要

The Shenington-Kirkpatrick model of spin glasses, the Hopfield model of neural networks and the Ising spin glass are all models of binary data belonging to the one-parameter exponential family with quadratic sufficient statistic. Under bare minimal conditions, we establish the root N-consistency of the maximum pseudolikelihood estimate of the natural parameter in this family, even at critical temperatures. Since very little is known about the low and critical temperature regimes of these extremely difficult models, the proof requires several new ideas. The author's version of Stein's method is a particularly useful tool. We aim to introduce these techniques into the realm of mathematical statistics through an example and present some open questions.