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The Papangelou process. A concept for Gibbs, Fermi and Bose processes. (English) Zbl 1302.60078

J. Contemp. Math. Anal., Armen. Acad. Sci. 46, No. 6, 326-337 (2011) and Izv. Nats. Akad. Nauk Armen., Mat. 46, No. 6, 49-66 (2011).
Summary: This note is a revised and enlarged version of the german article [the second author, ibid. 44, No. 1, 36–44 (2009); translation from Izv. Nats. Akad. Nauk Armen., Mat. 2009, No. 1, 45–52 (2009; Zbl 1302.60082)] in a slightly different framework. We here correct a serious mistake in the first version and generalize the class of Polya sum processes considered there. (A corrected version of the same results can be found already in the thesis of M. Rafler [Gaussian Loop- and Polya processes, apoint process approach. Potsdam: Universitätsverlag (PhD Thesis) (2009)].) Moreover, the class of Polya difference processes is constructed here for the first time. In analogy to classical statistical mechanics we propose a theory of interacting Bosons and Fermions. We consider Papangelou processes. These are point processes specified by some kernel which represents the conditional intensity of the process. The main result is a general construction of a large class of such processes which contains Cox, Gibbs processes of classical statistical mechanics, but also interacting Bose and Fermi processes.

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60G57 Random measures
60D05 Geometric probability and stochastic geometry

Citations:

Zbl 1302.60082
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References:

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