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 (σ λ), which is a general form of Gibbsianness. Under a continuity assumption, the Gibbsian conditional probabilities can be identified explicitly.
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Georgii, HO., Yoo, H.J. Conditional Intensity and Gibbsianness of Determinantal Point Processes. J Stat Phys 118, 55–84 (2005). https://doi.org/10.1007/s10955-004-8777-5
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DOI: https://doi.org/10.1007/s10955-004-8777-5