Advances in Applied Probability

Invariant distributions for shapes in sequences of randomly-divided rectangles

Francis K. C. Chen and Richard Cowan

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Interest has been shown in Markovian sequences of geometric shapes. Mostly the equations for invariant probability measures over shape space are extremely complicated and multidimensional. This paper deals with rectangles which have a simple one-dimensional shape descriptor. We explore the invariant distributions of shape under a variety of randomised rules for splitting the rectangle into two sub-rectangles, with numerous methods for selecting the next shape in sequence. Many explicit results emerge. These help to fill a vacant niche in shape theory, whilst contributing at the same time, new distributions on [0,1] and interesting examples of Markov processes or, in the language of another discipline, of stochastic dynamical systems.

Article information

Source
Adv. in Appl. Probab. Volume 31, Number 1 (1999), 1-14.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
http://projecteuclid.org/euclid.aap/1029954262

Digital Object Identifier
doi:10.1239/aap/1029954262

Mathematical Reviews number (MathSciNet)
MR1699657

Zentralblatt MATH identifier
0927.60008

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60E05: Distributions: general theory 60J05: Discrete-time Markov processes on general state spaces

Keywords
Invariant distributions shape stochastic geometry distribution theory Markov processes dynamical systems

Citation

Chen, Francis K. C.; Cowan, Richard. Invariant distributions for shapes in sequences of randomly-divided rectangles. Adv. in Appl. Probab. 31 (1999), no. 1, 1--14. doi:10.1239/aap/1029954262. http://projecteuclid.org/euclid.aap/1029954262.


Export citation