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A fascinating inverse problem that has been receiving considerable attention is the construction of realizations of random two-phase heterogeneous media with a target two-point correlation function. However, not every hypothetical two-point correlation function corresponds to a realizable two-phase medium. Here we collect all of the known necessary conditions on the two-point correlation functions scattered throughout a diverse literature and derive a new but simple positivity condition. We apply the necessary conditions to test the realizability of certain classes of proposed correlation functions.

Necessary Conditions on Realizable Two-Point Correlation Functions of Random Media