Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/40063

NONNORMAL APPROXIMATION BY STEIN'S METHOD OF EXCHANGEABLE PAIRS WITH APPLICATION TO THE CURIE-WEISS MODEL

Authors Chatterjee, Sourav
Shao, Qi-Man View this author's profile
Issue Date 2011
Source The Annals of applied probability , v. 21, (2), April 2011, p. 464-483
Summary where g(W) is a dominated term and r(W) is negligible. Let G(t) = f(0)(t)g(s)ds and define p(t) = c1e(-c0G(t)), where c(0) is a properly chosen constant and c(1) = 1/integral(infinity)(-infinity) e(-c0G(t)) dt. Let Y be a random variable with the probability density function p. It is proved that W converges to Y in distribution when the conditional second moment of (W - W') given W satisfies a law of large numbers. A Berry-Esseen type bound is also given. We use this technique to obtain a Berry-Esseen error bound of order 1/root n. in the noncentral limit theorem for the magnetization in the Curie Weiss ferromagnet at the critical temperature. Exponential approximation with application to the spectrum of the Bernoulli-Laplace Markov chain is also discussed.
Subjects
ISSN 1050-5164
Language English
Format Article
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