Translation-invariance of two-dimensional Gibbsian point processes

Details Translation-invariance of two-dimensional Gibbsian point processes Translation-invariance of two-dimensional Gibbsian point processes

2007-06-25

arxiv.org/abs/0706.3637v1

Mathematics

Probability

44 pages, 6 figures

Scientific paper

10.1007/s00220-007-0274-7

The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with two-body interaction, where the interesting cases of singular, hard-core and discontinuous interaction are included. We start with the special case of pure hard core repulsion in order to show how to treat hard cores in general.

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