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Title: Stein's method in high dimensions with applications
Authors: Röllin, A. 
Keywords: Curie-Weiss model
Gaussian interpolation
Last passage percolation on thin rectangles
Sherrington-Kirkpatrick model
Stein's method
Issue Date: May-2013
Citation: Röllin, A. (2013-05). Stein's method in high dimensions with applications. Annales de l'institut Henri Poincare (B) Probability and Statistics 49 (2) : 529-549. ScholarBank@NUS Repository.
Abstract: Let h be a three times partially differentiable function on Rn, let X = (X1, +⋯, Xn) be a collection of real-valued random variables and let Z = (Z1, +⋯, Zn) be a multivariate Gaussian vector. In this article, we develop Stein's method to give error bounds on the difference Eh(X) - Eh(Z) in cases where the coordinates of X are not necessarily independent, focusing on the high dimensional case n→∞. In order to express the dependency structure we use Stein couplings, which allows for a broad range of applications, such as classic occupancy, local dependence, Curie-Weiss model, etc. We will also give applications to the Sherrington-Kirkpatrick model and last passage percolation on thin rectangles. © 2013 Association des Publications de l'Institut Henri Poincaré.
Source Title: Annales de l'institut Henri Poincare (B) Probability and Statistics
ISSN: 02460203
DOI: 10.1214/11-AIHP473
Appears in Collections:Staff Publications

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