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February, 1995 A Triangle Inequality for Covariances of Binary FKG Random Variables
J. Van Den Berg, A. Gandolfi
Ann. Appl. Probab. 5(1): 322-326 (February, 1995). DOI: 10.1214/aoap/1177004843

Abstract

For binary random variables $\sigma_1, \sigma_2, \ldots, \sigma_n$ that satisfy the well-known FKG condition, we show that the variances and covariances satisfy $\operatorname{Var}(\sigma_j) \operatorname{Cov}(\sigma_i, \sigma_k) \geq \operatorname{Cov}(\sigma_i, \sigma_j)\operatorname{Cov}(\sigma_j, \sigma_k),\quad 1 \leq i, j, k \leq n.$ This generalizes and improves a result by Graham for ferromagnetic Ising models with nonnegative external fields.

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J. Van Den Berg. A. Gandolfi. "A Triangle Inequality for Covariances of Binary FKG Random Variables." Ann. Appl. Probab. 5 (1) 322 - 326, February, 1995. https://doi.org/10.1214/aoap/1177004843

Information

Published: February, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0841.60011
MathSciNet: MR1325056
Digital Object Identifier: 10.1214/aoap/1177004843

Subjects:
Primary: 60E15
Secondary: 60K35

Keywords: Correlation inequalities , correlation length , FKG inequality , Ising model

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 1 • February, 1995
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