Quasi-invariance and integration by parts for determinantal and permanental processes

Isabelle Camilier (1) , Laurent Decreusefond (1)

1 LTCI - Laboratoire Traitement et Communication de l'Information

Determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent. Their atoms exhibit mutual attraction of repulsion, thus these processes are very far from the uncorrelated situation encountered in Poisson models. We establish a quasi-invariance result : we show that if atoms locations are perturbed along a vector field, the resulting process is still a determinantal (respectively permanental) process, the law of which is absolutely continuous with respect to the original distribution. Based on this formula, following Bismut approach of Malliavin calculus, we then give an integration by parts formula.

Mots clés: Determinantal point processes; Malliavin calculus; permanental point processes; point processes; integration by parts formula

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Isabelle Camilier, Laurent Decreusefond. Quasi-invariance and integration by parts for determinantal and permanental processes. Journal of Functional Analysis, 2010, 259, pp.268-300. ⟨hal-00435496⟩