Conditional Intensity and Gibbsianness of Determinantal Point Processes

Abstract

The Papangelou intensities of determinantal (or fermion) point processes are investigated. These exhibit a monotonicity property expressing the repulsive nature of the interaction, and satisfy a bound implying stochastic domination by a Poisson point process. We also show that determinantal point processes satisfy the so-called condition $({\Sigma }_{\lambda })$ which is a general form of Gibbsianness. Under a continuity assumption, the Gibbsian conditional probabilities can be identified explicitly.

revised and extended

References in corpus (1)

• Gibbsianness of fermion random point fields

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