### 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 language | English (US) |
---|---|

Pages (from-to) | 75-80 |

Number of pages | 6 |

Journal | Communications in Mathematical Physics |

Volume | 91 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1983 |

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### 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.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 91, no. 1, pp. 75-80. https://doi.org/10.1007/BF01206051

}

TY - JOUR

T1 - A general central limit theorem for FKG systems

AU - Newman, Charles M.

PY - 1983/3

Y1 - 1983/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0002733273&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002733273&partnerID=8YFLogxK

U2 - 10.1007/BF01206051

DO - 10.1007/BF01206051

M3 - Article

AN - SCOPUS:0002733273

VL - 91

SP - 75

EP - 80

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -