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Conditional Intensity and Gibbsianness of Determinantal Point Processes

Probability 2010-03-16 v2 Mathematical Physics math.MP

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 (Σλ)(\Sigma_{\lambda}) which is a general form of Gibbsianness. Under a continuity assumption, the Gibbsian conditional probabilities can be identified explicitly.

Keywords

Cite

@article{arxiv.math/0401402,
  title  = {Conditional Intensity and Gibbsianness of Determinantal Point Processes},
  author = {Hans-Otto Georgii and Hyun Jae Yoo},
  journal= {arXiv preprint arXiv:math/0401402},
  year   = {2010}
}

Comments

revised and extended

R2 v1 2026-07-22T17:01:59.518Z