A general central limit theorem for FKG systems

Research output: Contribution to journalArticle

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

Fingerprint

Central limit theorem
FKG Inequality
theorems
Monotonic Function
Ferromagnet
Scaling Limit
Energy Density
Ising
Magnetization
Susceptibility
Random variable
random variables
Fixed point
flux density
magnetic permeability
scaling
magnetization
Model
temperature
Class

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

A general central limit theorem for FKG systems. / Newman, Charles M.

In: Communications in Mathematical Physics, Vol. 91, No. 1, 03.1983, p. 75-80.

Research output: Contribution to journalArticle

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