Stationary Determinantal Processes : Phase Transitions , Bernoullicity , Entropy , and Domination

Abstract

We study a class of stationary processes indexed by Z that are defined via minors of d-dimensional Toeplitz matrices. We obtain necessary and sufficient conditions for the existence of a phase transition (phase multiplicity) analogous to that which occurs in statistical mechanics. The absence of a phase transition is equivalent to the presence of a strong K… (More)

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