Existence of Gibbsian point processes with geometry-dependent interactions

Details Existence of Gibbsian point processes with geometry-dependent interactions Existence of Gibbsian point processes with geometry-dependent interactions

2010-03-15

arxiv.org/abs/1003.2875v1

Mathematics

Probability

25 pages

Scientific paper

We establish the existence of stationary Gibbsian point processes for interactions that act on hyperedges between the points. For example, such interactions can depend on Delaunay edges or triangles, cliques of Voronoi cells or clusters of $k$-nearest neighbors. The classical case of pair interactions is also included. The basic tools are an entropy bound and stationarity.

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