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Geodesics and flows in a Poissonian city
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Kendall, W. S. (2011) Geodesics and flows in a Poissonian city. Annals of Applied Probability, Vol.21 (No.3). pp. 801-842. doi:10.1214/10-AAP724 ISSN 1050-5164.
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Official URL: http://dx.doi.org/10.1214/10-AAP724
Abstract
The stationary isotropic Poisson line network was used to derive upper bounds
on mean excess network-geodesic length in Aldous and Kendall (2008). This new
paper presents a study of the geometry and fluctuations of near-geodesics in such
a network. The notion of a "Poissonian city" is introduced, in which connections
between pairs of nodes are made using simple "no-overshoot" paths based on the
Poisson line process. Asymptotics for geometric features and random variation in
length are computed for such near-geodesic paths; it is shown that they traverse the
network with an order of efficiency comparable to that of true network geodesics.
Mean characteristics and limiting behaviour at the centre are computed for a natural
network flow. Comparisons are drawn with similar network flows in a city based on
a comparable rectilinear grid. A concluding section discusses several open problems.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Geodesics (Mathematics), Poisson processes | ||||
Series Name: | Working papers | ||||
Journal or Publication Title: | Annals of Applied Probability | ||||
Publisher: | Institute of Mathematical Statistics | ||||
Place of Publication: | Coventry | ||||
ISSN: | 1050-5164 | ||||
Official Date: | June 2011 | ||||
Dates: |
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Volume: | Vol.21 | ||||
Number: | No.3 | ||||
Page Range: | pp. 801-842 | ||||
DOI: | 10.1214/10-AAP724 | ||||
Status: | Peer Reviewed | ||||
Date of first compliant deposit: | 17 December 2015 | ||||
Date of first compliant Open Access: | 17 December 2015 |
Data sourced from Thomson Reuters' Web of Knowledge
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Geodesics and flows in a Poissonian city. (deposited 04 Jul 2011 14:31)
- Geodesics and flows in a Poissonian city. (deposited 20 Sep 2011 11:59) [Currently Displayed]
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