Gibbsian representation for point processes via hyperedge potentials

10.10.2018, 10:15  –  Haus 9, Raum 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Benedikt Jahnel (WIAS)

Abstract: We consider marked point processes on the d-dimensional euclidean space, defined in terms of a quasilocal specification based on marked Poisson point processes. We investigate the possibility of constructing uniformly absolutely convergent Hamiltonians in terms of hyperedge potentials in the sense of Georgii and Dereudre. These potentials are natural generalizations of physical multibody potentials which are useful in models of stochastic geometry. With this we draw a link between the abstract theory of point processes in infinite volume, the study of measures under transformations, and statistical mechanics of systems of point particles.