Necessary and sufficient conditions for the existence of $\alpha$-determinantal processes

TL;DR

This paper establishes the exact conditions under which $\alpha$-determinantal processes exist and are infinitely divisible, utilizing results from multivariate negative binomial and binomial distributions.

Contribution

It provides the first complete characterization of existence and infinite divisibility conditions for $\alpha$-determinantal processes.

Findings

Derived necessary and sufficient conditions for existence.

Characterized infinite divisibility of $\alpha$-determinantal processes.

Connected $\alpha$-determinantal processes with multivariate distributions.

Abstract

We give necessary and sufficient conditions for existence and infinite divisibility of $\alpha$-determinantal processes. For that purpose we use results on negative binomial and ordinary binomial multivariate distributions.