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On the construction of point processes in statistical mechanics

  • We present a new approach to the construction of point processes of classical statistical mechanics as well as processes related to the Ginibre Bose gas of Brownian loops and to the dissolution in R-d of Ginibre's Fermi-Dirac gas of such loops. This approach is based on the cluster expansion method. We obtain the existence of Gibbs perturbations of a large class of point processes. Moreover, it is shown that certain "limiting Gibbs processes" are Gibbs in the sense of Dobrushin, Lanford, and Ruelle if the underlying potential is positive. Finally, Gibbs modifications of infinitely divisible point processes are shown to solve a new integration by parts formula if the underlying potential is positive.

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Metadaten
Author details:Benjamin Nehring, Suren PoghosyanGND, Hans ZessinORCiDGND
DOI:https://doi.org/10.1063/1.4807724
ISSN:0022-2488
Title of parent work (English):Journal of mathematical physics
Publisher:American Institute of Physics
Place of publishing:Melville
Publication type:Article
Language:English
Year of first publication:2013
Publication year:2013
Release date:2017/03/26
Volume:54
Issue:6
Number of pages:15
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer review:Referiert
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