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A polyhedral Markov field - pushing the Arak-Surgailis construction into three dimensions

Tomasz Schreiber
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Abstract

The purpose of the paper is to construct a polyhedral Markov field in ${\mathbb R}^3$ in analogy with the planar construction of the original Arak (1982) polygonal Markov field. We provide a dynamic construction of the process in terms of evolution of two-dimensional multi-edge systems tracing polyhedral boundaries of the field in three-dimensional time-space. We also give a general algorithm for simulating Gibbsian modifications of the constructed polyhedral field.

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Tomasz Schreiber. 2007-06-21. A polyhedral Markov field - pushing the Arak-Surgailis construction into three dimensions. https://arxiv.org/abs/math/0503429

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