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October 2007 Estimation in spin glasses: A first step
Sourav Chatterjee
Ann. Statist. 35(5): 1931-1946 (October 2007). DOI: 10.1214/009053607000000109


The Sherrington–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 $\sqrt{N}$-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.


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Sourav Chatterjee. "Estimation in spin glasses: A first step." Ann. Statist. 35 (5) 1931 - 1946, October 2007.


Published: October 2007
First available in Project Euclid: 7 November 2007

zbMATH: 1126.62128
MathSciNet: MR2363958
Digital Object Identifier: 10.1214/009053607000000109

Primary: 60K35, 62F10, 62F12, 82B44

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.35 • No. 5 • October 2007
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