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

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