A Gibbs point process of diffusions: existence and uniqueness

Autoren: Alexander Zass (2020)

In this work we consider a system of infinitely many interacting diffusions as a marked Gibbs point process. With this perspective, we show, for a large class of stable and regular interactions, existence and (conjecture) uniqueness of an infinite-volume Gibbs process. In order to prove existence we use the specific entropy as a tightness tool. For the uniqueness problem, we use cluster expansion to prove a Ruelle bound, and conjecture how this would lead to the uniqueness of the Gibbs process as solution of the Kirkwood-Salsburg equation.

Zeitschrift:
Lectures in Pure and Applied Mathematics
Verlag:
Potsdam University Press
Buchtitel:
Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics
Seiten:
13-22
Band:
6

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