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.
Author details: | Benjamin Nehring, Suren PoghosyanGND, Hans ZessinORCiDGND |
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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 |