Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
We present some results on the existence and uniqueness of marked Gibbs point processes. Firstly, we prove in a general setting the existence of an infinite-volume marked Gibbs point process, via the so-called entropy method from large deviations theory. We then adapt it to the setting of infinite-dimensional Langevin diffusions, put in interaction via a Gibbsian description; we also obtain the uniqueness of such a Gibbs process via cluster expansion techniques. Finally, we explore the question of uniqueness in the case of repulsive interactions, in a novel approach to uniqueness by applying the discrete Dobrushin criterion to the continuum framework.
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