Electronic Communications in Probability

A Cramér type moderate deviation theorem for the critical Curie-Weiss model

Van Hao Can and Viet-Hung Pham

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Limit theorems for the magnetization of Curie-Weiss model have been studied extensively by Ellis and Newman. To refine these results, Chen, Fang and Shao prove Cramér type moderate deviation theorems for non-critical cases by using Stein method. In this paper, we consider the same question for the remaining case - the critical Curie-Weiss model. By direct and simple arguments based on Laplace method, we provide an explicit formula of the error and deduce a Cramér type result.

Article information

Electron. Commun. Probab., Volume 22 (2017), paper no. 62, 12 pp.

Received: 26 June 2017
Accepted: 27 October 2017
First available in Project Euclid: 15 November 2017

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Primary: 60F10: Large deviations 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

Cramér type moderate deviation Curie-Weiss model

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Can, Van Hao; Pham, Viet-Hung. A Cramér type moderate deviation theorem for the critical Curie-Weiss model. Electron. Commun. Probab. 22 (2017), paper no. 62, 12 pp. doi:10.1214/17-ECP96. https://projecteuclid.org/euclid.ecp/1510736419

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