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Stein's Method for Dependent Random Variables Occuring in Statistical Mechanics

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Stein's Method for Dependent Random Variables Occuring in Statistical Mechanics
2.	Creator	Author's name, affiliation, country	Peter Eichelsbacher; Ruhr University of Bochum; Germany
2.	Creator	Author's name, affiliation, country	Matthias Loewe; University of Muenster; Germany
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Berry-Esseen bound, Stein's method, exchangeable pairs, Curie Weiss models, critical temperature, GHS-inequality
3.	Subject	Subject classification	60F05, 82B20, 82B26
4.	Description	Abstract	We develop Stein's method for exchangeable pairs for a rich class of distributional approximations including the Gaussian distributions as well as the non-Gaussian limit distributions. As a consequence we obtain convergence rates in limit theorems of partial sums for certain sequences of dependent, identically distributed random variables which arise naturally in statistical mechanics, in particular in the context of the Curie-Weiss models. Our results include a Berry-Esseen rate in the Central Limit Theorem for the total magnetization in the classical Curie-Weiss model, for high temperatures as well as at the critical temperature, where the Central Limit Theorem fails. Moreover, we analyze Berry-Esseen bounds as the temperature converges to one and obtain a threshold for the speed of this convergence. Single spin distributions satisfying the Griffiths-Hurst-Sherman (GHS) inequality like models of liquid helium or continuous Curie-Weiss models are considered.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	SFB/TR 12 and Mathematisches Forschungsinstitut Oberwolfach
7.	Date	(YYYY-MM-DD)	2010-06-28
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/777
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-777
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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