Existence of Gibbs measure for a model of T-tessellations

Details Existence of Gibbs measure for a model of T-tessellations Existence of Gibbs measure for a model of T-tessellations

2010-12-10

arxiv.org/abs/1012.2182v1

Mathematics

Probability

22 pages

Scientific paper

T-tessellations are polygonal tessellations where all vertices are T-shaped. This kind of tessellation often appear in man-made environments such as plots of land. Adamczyk and Ki\^eu have developed a stochastic model for generating these tessellations. Unlike former proposals, adding an energy allows to favour even long-range correlations. For example, the cells could be biased to have similar areas. The flip-side, apart from harder simulations, is that the measure was not proven to be finite, and thus the model was not proven to be well-defined. This article proves that these measures are finite, by bounding from above the number of different possible T-tessellations on $k$ fixed lines.

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