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Point-based polygonal models for random graphs

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

T. Arak ,
P. Clifford  and
D. Surgailis
T. Arak*
Affiliation:
Chalmers University of Technology
P. Clifford*
Affiliation:
University of Oxford
D. Surgailis*
Affiliation:
Institute of Mathematics and Informatics, Vilnius
*
∗Postal address: School of Mathematics and Computing Sciences, Chalmers University of Technology, S-41296 Göteborg, Sweden.
∗∗Postal address: Department of Statistics, 1 South Parks Road, Oxford OX1 3TG.
∗∗∗Institute of Mathematics and Informatics, 232600 Vilnius, Akademijos 4, Lithuania.
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Abstract

We define a class of two-dimensional Markov random graphs with I, V, T and Y-shaped nodes (vertices). These are termed polygonal models. The construction extends our earlier work [1]– [5]. Most of the paper is concerned with consistent polygonal models which are both stationary and isotropic and which admit an alternative description in terms of the trajectories in space and time of a one-dimensional particle system with motion, birth, death and branching. Examples of computer simulations based on this description are given.

Keywords

MARKOV GRAPHSCONSISTENT MODELSPARTICLE SYSTEMSPOISSON SEGMENT PROCESSPOLYMERIZATION

MSC classification

Primary: 60G60: Random fields
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 2 , June 1993 , pp. 348 - 372
Copyright
Copyright © Applied Probability Trust 1993 

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