For binary random variables σ1,σ2,…,σn that satisfy the well-known FKG condition, we show that the variances and covariances satisfy Var(σj)Cov(σi,σk)≥Cov(σi,σj)Cov(σj,σk),1≤i,j,k≤n. This generalizes and improves a result by Graham for ferromagnetic Ising models with nonnegative external fields.
A triangle inequality for covariances of binary FKG random variables / J. v. den Berg; A. Gandolfi. - In: THE ANNALS OF APPLIED PROBABILITY. - ISSN 1050-5164. - STAMPA. - 5:(1995), pp. 322-326. [10.1214/aoap/1177004843]
A triangle inequality for covariances of binary FKG random variables
GANDOLFI, ALBERTO
1995
Abstract
For binary random variables σ1,σ2,…,σn that satisfy the well-known FKG condition, we show that the variances and covariances satisfy Var(σj)Cov(σi,σk)≥Cov(σi,σj)Cov(σj,σk),1≤i,j,k≤n. This generalizes and improves a result by Graham for ferromagnetic Ising models with nonnegative external fields.
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