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dc.contributor.authorEichelsbacher, Peter
dc.contributor.authorLöwe, Matthias
dc.date.accessioned2009-03-20T12:00:30Z
dc.date.accessioned2016-10-05T14:14:11Z
dc.date.available2009-03-20T12:00:30Z
dc.date.available2016-10-05T14:14:11Z
dc.date.issued2009-03-03
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1143
dc.descriptionResearch in Pairs 2008en_US
dc.description.abstractWe obtain rates of convergence in limit theorems of partial sums $S_n$ 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. Under appropriate assumptions there exists a real number $\alpha$, a positive number $\mu$, and a positive integer $k$ such that $(S_n-n\alpha)/n^{1-1/2k}$ converges weakly to a random variable with density proportional to $exp(-\mu|x|^{2k}/(2k)!)$. 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 with density proportional to $exp(-\mu|x|^{2k}/(2k)!)$. Our results include the optimal 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 $\beta_c=1$, where the Central Limit Theorem fails. Moreover, we analyze Berry-Esseen bounds as the temperature $1/\beta_n$ 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.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2009,09
dc.subjectBerry-Esseen bounden_US
dc.subjectStein's methoden_US
dc.subjectexchangeable pairsen_US
dc.subjectCurie-Weiss modelsen_US
dc.subjectcritical temperatureen_US
dc.subjectGHS-inequalityen_US
dc.titleStein's method for dependent random variables occuring in statistical mechanicsen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2009-09
local.scientificprogramResearch in Pairs 2008
local.series.idOWP-2009-09
local.subject.msc60
local.subject.msc82
dc.identifier.urnurn:nbn:de:101:1-2009042383
dc.identifier.ppn1649512430


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