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A general central limit theorem for FKG systems

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Abstract

A central limit theorem is given which is applicable to (not necessarily monotonic) functions of random variables satisfying the FKG inequalities. One consequence is convergence of the block spin scaling limit for the magnetization and energy densities (jointly) to the infinite temperature fixed point of independent Gaussian blocks for a large class of Ising ferromagnets whenever the susceptibility is finite. Another consequence is a central limit theorem for the density of thesurface of the infinite cluster in percolation models.

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Authors and Affiliations

  1. Department of Mathematics, The University of Arizona, 85721, Tucson, AZ, USA

    Charles M. Newman

  2. Institute of Mathematics and Computer Science, The Hebrew University of Jerusalem, Givat Ram, IL-91904, Jerusalem, Israel

    Charles M. Newman

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  1. Charles M. Newman
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Communicated by J. Fröhlich

Research supported in part by the National Science Foundation under grant No. MCS 80-19384

Temporary address until July, 1983

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Newman, C.M. A general central limit theorem for FKG systems. Commun.Math. Phys. 91, 75–80 (1983). https://doi.org/10.1007/BF01206051

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  • DOI: https://doi.org/10.1007/BF01206051

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