English

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

Probability 2007-06-21 v2

Abstract

The purpose of the paper is to construct a polyhedral Markov field in R3{\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.

Cite

@article{arxiv.math/0503429,
  title  = {A polyhedral Markov field - pushing the Arak-Surgailis construction into three dimensions},
  author = {Tomasz Schreiber},
  journal= {arXiv preprint arXiv:math/0503429},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T17:17:00.605Z