English

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 kk-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

R2 v1 2026-06-21T14:57:52.914Z