Critical fluctuations of sums of weakly dependent random vectors
type: Item
instance of: scholarly article
title: Critical fluctuations of sums of weakly dependent random vectors
zbMATH Open document ID: 0792.60026
DOI: 10.1007/BF01192515
author: Kongming Wang
publication date: 1994-07-14T00:00:00Z
review text: Let \(S_ n\) be sums of i.i.d. random vectors taking values in a Banach space and \(F\) be a smooth function. We study the fluctuations of \(S_ n\) under the transformed measure \(P_ n\) given by \(dP_ n/dP=\exp (nF(S_ n/n))/Z_ n\). If degeneracy occurs, then the projection of \(S_ n\) onto the degenerate subspace, properly centered and scaled, converges to a non-Gaussian probability measure with the degenerate subspace as its support. The projection of \(S_ n\) onto the non-degenerate subspace, scaled with the usual order \(\sqrt n\), converges to a Gaussian probability measure with the non-degenerate subspace as its support. The two projective limits are in general dependent. We apply this theory to the critical mean field Heisenberg model and prove a central limit type theorem for the empirical measure of this model.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60B12
zbMATH DE Number: 569016
zbMATH Keywords: Gaussian probability measure
zbMATH Keywords: critical mean field Heisenberg model
zbMATH Keywords: central limit type theorem
zbMATH Keywords: empirical measure
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569016