Communications in Mathematical Physics

, Volume 91, Issue 1, pp 75–80 | Cite as

A general central limit theorem for FKG systems

  • Charles M. Newman


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.


Neural Network Statistical Physic Energy Density Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Charles M. Newman
    • 1
    • 2
  1. 1.Department of MathematicsThe University of ArizonaTucsonUSA
  2. 2.Institute of Mathematics and Computer ScienceThe Hebrew University of JerusalemJerusalemIsrael

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