An extension of Dobrushin's uniqueness criterion and applications to Gibbs point processes

Tanja Pasurek, Universität Bielefeld, Germany

We extend the classical Dobrushin's uniqueness criterion to Markov random fields on general graphs and with single-spin spaces that need not be locally compact. As a by-product of the method, we establish the exponential decay of correlations in the uniqueness regime. The applicability of the theory will be shown for continuous particle systems (with possibly non-trivial internal structure), including Gibbs fields on (marked) configurations. In conclusion, we touch upon a complementary question about the multiplicity (phase transition) in such models.

Based on joint work with Yuri Kondratiev and Michael Röckner.

Invited by Sylvie Roelly