Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Suren Poghosyan (Nat. Acad. of Science, Armenia)
For a pair potential Φ in a general underlying space X satisfying some natural and sufficiently general
conditions we define by means of the so called Ursell kernel a function r which is shown to be the corre-
lation function of a unique process Q, the limiting Gibbs process for Φ with empty boundary conditions.
This process is exhibited as a Gibbs process in the sense of Dobrushin, Lanford and Ruelle for a class of
pair potentials, which contains classical stable (in particular positive) and hard-core potentials that we
call Penrose potentials. For some class of Penrose potentials we show that Q is the unique Gibbs process
for Φ. We use the classical method of Kirkwood-Salsburg equations.
This is a joint work with Hans Zessin.
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