Advances in Applied Probability

The permanental process

Peter McCullagh and Jesper Møller

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We extend the boson process first to a large class of Cox processes and second to an even larger class of infinitely divisible point processes. Density and moment results are studied in detail. These results are obtained in closed form as weighted permanents, so the extension is called a permanental process. Temporal extensions and a particularly tractable case of the permanental process are also studied. Extensions of the fermion process along similar lines, leading to so-called determinantal processes, are discussed.

Article information

Adv. in Appl. Probab. Volume 38, Number 4 (2006), 873-888.

First available in Project Euclid: 6 December 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes
Secondary: 62M30: Spatial processes

Boson process Cox process density of spatial point process determinantal process factorial moment measure fermion process Gaussian process infinite divisibility simulation spatio-temporal process weighted permanent


McCullagh, Peter; Møller, Jesper. The permanental process. Adv. in Appl. Probab. 38 (2006), no. 4, 873--888.

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