Necessary and sufficient conditions for the existence of -determinantal processes
نویسنده
چکیده
We give necessary and sufficient conditions for existence and infinite divisibility of α-determinantal processes. For that purpose we use results on negative binomial and ordinary binomial multivariate distributions.
منابع مشابه
On the Construction of Particle Distributions with Specified Single and Pair Densities†
We discuss necessary conditions for the existence of a probability distribution on particle configurations in d-dimensions, i.e., a point process, compatible with a specified density F and radial distribution function g(r). In d ) 1 we give necessary and sufficient criteria on Fg(r) for the existence of such a point process of renewal (Markov) type. We prove that these conditions are satisfied ...
متن کاملStationary Determinantal Processes : Phase Transitions , Bernoullicity , Entropy , and Domination by
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 property, a particular strengthening ...
متن کاملStationary determinantal processes: Phase transitions, Bernoullicity, domination, and entropy
We study a class of stationary processes indexed by Z that are defined via minors of d-dimensional (multilevel) Toeplitz matrices. We obtain necessary and sufficient conditions for phase multiplicity (the existence of a phase transition) analogous to that which occurs in statistical mechanics. Phase uniqueness is equivalent to the presence of a strong K property, a particular strengthening of t...
متن کاملStationary Determinantal Processes : Phase Transitions , Bernoullicity , Entropy , and Domination
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 property, a particular strengthening ...
متن کاملStationary Determinantal Processes: Phase Multiplicity, Bernoullicity, Entropy, and Domination
We study a class of stationary processes indexed by Z that are defined via minors of d-dimensional (multilevel) Toeplitz matrices. We obtain necessary and sufficient conditions for phase multiplicity (the existence of a phase transition) analogous to that which occurs in statistical mechanics. Phase uniqueness is equivalent to the presence of a strong K property, a particular strengthening of t...
متن کامل