Existence of Gibbsian point processes with geometry-dependent interactions
Probability
2010-03-16 v1 Mathematical Physics
math.MP
Abstract
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 -nearest neighbors. The classical case of pair interactions is also included. The basic tools are an entropy bound and stationarity.
Keywords
Cite
@article{arxiv.1003.2875,
title = {Existence of Gibbsian point processes with geometry-dependent interactions},
author = {David Dereudre and Remy Drouilhet and Hans-Otto Georgii},
journal= {arXiv preprint arXiv:1003.2875},
year = {2010}
}
Comments
25 pages