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

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

2005-03-21

arxiv.org/abs/math/0503429v2

Markov Processes and Related Fields (2006), vol. 12 (1), 43-58

Mathematics

Probability

16 pages, second corrected version, published in the Markov Processes and Related Fields (2006), vol. 12 (1), 43-58, further s

Scientific paper

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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