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.
Citation
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
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