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arxiv: math/0401402 · v2 · submitted 2004-01-28 · 🧮 math.PR · math-ph· math.MP

Conditional Intensity and Gibbsianness of Determinantal Point Processes

classification 🧮 math.PR math-phmath.MP
keywords pointdeterminantalprocessesconditionalgibbsiannesssatisfyassumptionbound
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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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