Marked Gibbs Point Processes with Unbounded Interaction: An Existence Result
Marked Gibbs Point Processes with Unbounded Interaction: An Existence Result
We construct marked Gibbs point processes in $\mathbb{R}^d$ under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical interaction admits an a.s. finite but random range. Secondly, the random marks -- attached to …