5 problems

Consider the Quermass interaction for a finite configuration $omega$ of points, given by … where $\theta_{d-k}\in\mathbb{R}$, $M_k^d$ is the $k$-th Minkowski functional, and…

The model is a Gibbs point process with Quermass interaction, whose parameters include the activity and inverse temperature, and suppose that the first-order phase transition estab…

Let $\phi$ be a pair potential satisfying assumptions (A2) and (A3), with activity $z$ and inverse temperature $\beta$. A Gibbs measure is a probability measure describing the equi…

The maximum pseudolikelihood estimator (MPLE) is used to estimate parameters of Gibbs point process models, and the pair potential is evaluated numerically, including through the B…

Residuals are constructed from stationary marked Gibbs point processes using test functions and are evaluated over an expanding sampling window. A strong law of large numbers descr…