A polyhedral Markov field - pushing the Arak-Surgailis construction into three dimensions
Abstract
The purpose of the paper is to construct a polyhedral Markov field in R3 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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