The Library
Rayleigh random flights on the Poisson line SIRSN
Tools
Tools
Tools
Kendall, W. S. (2020) Rayleigh random flights on the Poisson line SIRSN. Electronic Journal of Probability, 25 . pp. 1-36. 124. doi:10.1214/20-EJP526 ISSN 1083-6489.
|
PDF
WRAP-Rayleigh-random-flights-Poisson-line-SIRSN-Kendall-2020.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (975Kb) | Preview |
|
![[img]](https://wrap.warwick.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
WRAP-Rayleigh-random-flights-Poisson-line-SIRSN-Kendall-2020.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (400Kb) |
Official URL: http://dx.doi.org/10.1214/20-EJP526
Abstract
We study scale-invariant Rayleigh Random Flights (“RRF”) in random environments given by planar Scale-Invariant Random Spatial Networks (“SIRSN”) based on speed-marked Poisson line processes. A natural one-parameter family of such RRF (with scale-invariant dynamics) can be viewed as producing “randomly-broken local geodesics” on the SIRSN; we aim to shed some light on a conjecture that a (non-broken) geodesic on such a SIRSN will never come to a complete stop en route. (If true, then all such geodesics can be represented as doubly-infinite sequences of sequentially connected line segments. This would justify a natural procedure for computing geodesics.) The family of these RRF (“SIRSN-RRF”), is introduced via a novel axiomatic theory of abstract scattering representations for Markov chains (itself of independent interest). Palm conditioning (specifically the Mecke-Slivnyak theorem for Palm probabilities of Poisson point processes) and ideas from the ergodic theory of random walks in random environments are used to show that at a critical value of the parameter the speed of the scale-invariant SIRSN-RRF neither diverges to infinity nor tends to zero, thus supporting the conjecture.
| Item Type: | Journal Article | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | |||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||
| Library of Congress Subject Headings (LCSH): | Probabilities, Scattering (Mathematics), Dirichlet forms, Poisson processes | |||||||||||||||
| Journal or Publication Title: | Electronic Journal of Probability | |||||||||||||||
| Publisher: | University of Washington. Dept. of Mathematics | |||||||||||||||
| ISSN: | 1083-6489 | |||||||||||||||
| Official Date: | 2020 | |||||||||||||||
| Dates: |
|
|||||||||||||||
| Volume: | 25 | |||||||||||||||
| Page Range: | pp. 1-36 | |||||||||||||||
| Article Number: | 124 | |||||||||||||||
| DOI: | 10.1214/20-EJP526 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||
| Date of first compliant deposit: | 9 October 2020 | |||||||||||||||
| Date of first compliant Open Access: | 12 October 2020 | |||||||||||||||
| RIOXX Funder/Project Grant: |
|
|||||||||||||||
| Related URLs: |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
