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On the Gaussian fluctuations of the critical Curie-Weiss model in statistical mechanics. (English) Zbl 0684.60080
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.
Reviewer: V.Tigoiu

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F05 Central limit and other weak theorems
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References:
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