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 the surface of the infinite cluster in percolation models.

Original languageEnglish (US)
Pages (from-to)75-80
Number of pages6
JournalCommunications In Mathematical Physics
Volume91
Issue number1
DOIs
StatePublished - Mar 1983

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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