Marked Gibbs point processes with unbounded interaction: an existence result

Sylvie Roelly, Alexander Zass

Published 2019-11-28Version 1

We construct marked Gibbs point processes on $\mathbb{R}^d$ under quite general assumptions. Firstly, the interaction functional may be unbounded and its range is not assumed to be uniformly bounded. Indeed, our typical interaction admits an a.s. finite but random range. Secondly, the random marks belong to a general normed space $\mathcal{S}$. They are not bounded, but their law should admit a super-exponential moment.