Conditional Intensity and Gibbsianness of Determinantal Point Processes

Details Conditional Intensity and Gibbsianness of Determinantal Point Processes Conditional Intensity and Gibbsianness of Determinantal Point Processes

2004-01-28

arxiv.org/abs/math/0401402v2

J. Statist. Phys. 118, 55-84 (2005)

Mathematics

Probability

revised and extended

Scientific paper

10.1007/s10955-004-8777-5

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.

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