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Critical fluctuations of sums of weakly dependent random vectors
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  • Published: June 1994

Critical fluctuations of sums of weakly dependent random vectors

  • Kongming Wang1 nAff2 

Probability Theory and Related Fields volume 98, pages 229–243 (1994)Cite this article

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Summary

LetS n be sums of iid random vectors taking values in a Banach space andF be a smooth function. We study the fluctuations ofS n under the transformed measureP n given byd P n/d P=exp (nF(S n/n))/Z n. If degeneracy occurs then the projection ofS 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 ofS 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.

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Author notes
  1. Kongming Wang

    Present address: Institute of Social and Preventive Medicine, University of Zürich, Sumatrastraße 30, CH-8006, Zürich, Switzerland

Authors and Affiliations

  1. Institute of Applied Mathematics, University of Zürich, Rämistrasse 74, CH-8001, Zürich, Switzerland

    Kongming Wang

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  1. Kongming Wang
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Supported by a grant from the Swiss National Science Foundation (21–29833.90)

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Wang, K. Critical fluctuations of sums of weakly dependent random vectors. Probab. Th. Rel. Fields 98, 229–243 (1994). https://doi.org/10.1007/BF01192515

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  • Received: 01 March 1993

  • Revised: 09 November 1993

  • Issue Date: June 1994

  • DOI: https://doi.org/10.1007/BF01192515

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Mathematics Subject Classificantion (1991)

  • 60F10
  • 60B12
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