A polyhedral Markov field - pushing the Arak-Surgailis construction into three dimensions
Abstract
Description
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.
16 pages, second corrected version, published in the Markov Processes and Related Fields (2006), vol. 12 (1), 43-58, further small corrections
16 pages, second corrected version, published in the Markov Processes and Related Fields (2006), vol. 12 (1), 43-58, further small corrections