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 ${\mathbb R}^3$ 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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- March 2005
- DOI:
- arXiv:
- arXiv:math/0503429
- Bibcode:
- 2005math......3429S
- Keywords:
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- Mathematics - Probability;
- 60D05;
- 60K35;
- 82B21
- E-Print:
- 16 pages, second corrected version, published in the Markov Processes and Related Fields (2006), vol. 12 (1), 43-58, further small corrections