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June 2016 Planar tessellations that have the half-Gilbert structure
James Burridge, Richard Cowan
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Adv. in Appl. Probab. 48(2): 574-584 (June 2016).

Abstract

In the full rectangular version of Gilbert's planar tessellation (see Gilbert (1967), Mackisack and Miles (1996), and Burridge et al. (2013)), lines extend either horizontally (with east- and west-growing rays) or vertically (north- and south-growing rays) from seed points which form a stationary Poisson point process, each ray stopping when it meets another ray that has blocked its path. In the half-Gilbert rectangular version, east- and south-growing rays, whilst having the potential to block each other, do not interact with west and north rays, and vice versa. East- and south-growing rays have a reciprocality of blocking, as do west and north. In this paper we significantly expand and simplify the half-Gilbert analytic results that we gave in Burridge et al. (2013). We also show how the idea of reciprocality of blocking between rays can be used in a much wider context, with rays not necessarily orthogonal and with seeds that produce more than two rays.

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James Burridge. Richard Cowan. "Planar tessellations that have the half-Gilbert structure." Adv. in Appl. Probab. 48 (2) 574 - 584, June 2016.

Information

Published: June 2016
First available in Project Euclid: 9 June 2016

zbMATH: 1344.60014
MathSciNet: MR3511776

Subjects:
Primary: 05B45 , 60D05
Secondary: 51M20 , 60G55

Keywords: crack formation , division of space , point process , random tessellation

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 2 • June 2016
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