Stein's Method of Exchangeable Pairs with Application to the Curie-Weiss Model

Let (W,W ′) be an exchangeable pair. Assume that E(W − W ′|W ) = g(W ) + r(W ), where g(W ) is a dominated term while r(W ) is negligible. Let G(t) = ∫ t 0 g(s)ds and define p(t) = c1e −c0G(t), where c0 is a properly chosen constant and c1 = 1/ ∫∞ −∞ p(t)dt . Let Y be a random variable with the probability density function p. In this talk we shall proved that W converges to Y in distribution under certain regular conditions. A Berry-Esseen type bound is also given. An application to the Curie-Weiss model will be discussed. The talk is based on a joint work with Sourav Chatterjee.

• Publication year

  2009

• Venue

  Unknown venue

• Publication date

  2009-07-25

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1214/10-AAP712arXiv 0907.4450
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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