On the construction of point processes in statistical mechanics

• Main Authors: Nehring, Benjamin, Poghosyan, Suren, Zessin, Hans
• Format: Others
• Language: English
• Published: Universität Potsdam 2013
• Subjects: Levy measure; cluster expansion; Gibbs perturbation; DLR equation; Mathematics
• Online Access: http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64080; http://opus.kobv.de/ubp/volltexte/2013/6408/

By means of the cluster expansion method we show that a recent result of Poghosyan and Ueltschi (2009) combined with a result of Nehring (2012) yields a 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. The latter will be identified as a Gibbs perturbation of the ideal Fermi gas. On generalizing these considerations we will obtain the existence of a large class of Gibbs perturbations of the so-called KMM-processes as they were introduced by Nehring (2012). 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. And finally, Gibbs modifications of infinitely divisible point processes are shown to solve a new integration by parts formula if the underlying potential is positive.