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Kendall, W. S. (2014) Lines and networks. Markov Processes and Related Fields, Volume 20 (Number 1). pp. 81-106.
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Official URL: http://mech.math.msu.su/~malyshev/cont13.htm
Abstract
The theory of random lines has a celebrated history, reaching back 300 years into the past to the work of Buffon, and forming a major part of the field of stochastic geometry. Recently it has found application in the derivation of surprising non-stochastic results concerning effective planar networks [D.J. Aldous and W.S. Kendall, Short-length routes in low-cost networks via Poisson line patterns. Adv. Appl. Probab., 2008, v.40, N1, 1-21].
The following is an account corresponding to three lectures on this material, including a very brief introduction to the relevant stochastic geometry, and also a description of some more recent work concerning flows in related networks [W.S. Kendall, Networks and Poisson line patterns: fluctuation asymptotics. Oberwolfach Rep., 2008, v.5, N4, 2670-2672; Geodesics and flows in a Poissonian city. Ann. Appl. Probab., 2011, v.21, N3, 801-842] as well as a rather curious random metric space.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science > Statistics | ||||
| Journal or Publication Title: | Markov Processes and Related Fields | ||||
| Publisher: | Polomat | ||||
| ISSN: | 1024-2953 | ||||
| Official Date: | 2014 | ||||
| Dates: |
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| Volume: | Volume 20 | ||||
| Number: | Number 1 | ||||
| Page Range: | pp. 81-106 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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