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

Franck Maunoury (1, 2, 3, 4, 5)

1 UPMC - Université Pierre et Marie Curie - Paris 6
2 UPD7 - Université Paris Diderot - Paris 7
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
4 Télécom ParisTech
5 LTCI - Laboratoire Traitement et Communication de l'Information

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.

Mots clés: determinantal process; permanental process; α-determinantal process; complete monotonicity; fermion process; boson process; infinitely divisible; α-permanental process

Domaines: Probabilités [math.PR]

Franck Maunoury. Necessary and sufficient conditions for the existence of $\alpha$-determinantal processes. Séminaire de Probabilités, 2015, XLVIII, pp.423-444. ⟨hal-01215176⟩