On the "triangular" inequality in the theory of two-phase random media

Abstract

A necessary condition on the two-point correlation function of binary random media, noticed by Matheron [1] and called by him "triangular" inequality, is studied in this note. An appropriate result, due to Achiezer and Glazman [2], is first recalled. Simple consequences of this inequality are given, as well as a necessary condition for its validity in a statistically isotropic medium. It is shown that it represents a requirement, independent of that of the familiar positive definiteness, that should be additionally imposed on the two-point correlation function of any realistic binary medium.