Determinantal processes

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. These processes
are thus very far from the uncorrelated situation encountered in Poisson
models.

Quasi-invariance

In the linked paper, 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.

Ornstein-Uhlenbeck processes

We are now interested in Ornstein-Uhlenbeck associated to determinantal point processes.