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

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

2009-11-24

arxiv.org/abs/0911.4638v1

Journal of Functional Analysis 259 (2010) 268-300

Mathematics

Probability

Journal of Functional Analysis (2010) To appear

Scientific paper

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.

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