On the Gaussian fluctuations of the critical Curie-Weiss model in statistical mechanics
type: Item
instance of: scholarly article
title: On the Gaussian fluctuations of the critical Curie-Weiss model in statistical mechanics
zbMATH Open document ID: 0684.60080
DOI: 10.1007/BF00333150
author: F. Papangelou
publication date: 1989-01-01T00:00:00Z
review text: It is known, due to some recent results, that the fluctuations of the critical Curie-Weiss model are not Gaussian. In this paper the author shows that for a large class of probability measures \(\rho\) there is considerable Gaussian structure in the internal fluctuations of the critical model. In the Curie-Weiss model all large subsystems fluctuate and the implications of this can be described in terms of weak convergence in the space of paths. The main result of this paper is focussed on fluctuations of the error term, which may be called the second order fluctuations. It is proved that the second order fluctuations are asymptotically those of a Brownian bridge collapsing to the t-axis, and on the other hand, that the polygonal process converges in distribution to a Brownian motion with randomised shift Y.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 4121186
zbMATH Keywords: Curie-Weiss model
zbMATH Keywords: internal fluctuations of the critical model
zbMATH Keywords: large subsystems
zbMATH Keywords: second order fluctuations
MaRDI profile type: Publication
cites work: Q5560061
cites work: Limit theorems in the area of large deviations for some dependent random variables
cites work: Nucleation for a long range magnetic model
cites work: Symmetry breaking and random waves for magnetic systems on a circle
cites work: Q3681702
cites work: Limit theorems for sums of dependent random variables occurring in statistical mechanics
cites work: Q5533878
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 4121186