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

Abstract 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 atom 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.

• Publication year

  2009

• Venue

  Journal of Functional Analysis

• Publication date

  2009-11-24

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1016/J.JFA.2010.01.007arXiv 0911.4638
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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