On the One Dimensional Poisson Random Geometric Graph
Given a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process, and edges exist between two points if and only if their distance is less than a fixed given threshold. We compute explicitly the distribution of the number of...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2011/350382 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832552644347953152 |
|---|---|
| author | L. Decreusefond E. Ferraz |
| author_facet | L. Decreusefond E. Ferraz |
| author_sort | L. Decreusefond |
| collection | DOAJ |
| description | Given a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process, and edges exist between two points if and only if their distance is less than a fixed given threshold. We compute explicitly the distribution of the number of connected components of this graph. The proof relies on inverting some Laplace transforms. |
| format | Article |
| id | doaj-art-611e1c14026744b0aff7f9944be99db2 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-611e1c14026744b0aff7f9944be99db22025-02-03T05:58:08ZengWileyJournal of Probability and Statistics1687-952X1687-95382011-01-01201110.1155/2011/350382350382On the One Dimensional Poisson Random Geometric GraphL. Decreusefond0E. Ferraz1Institut Télécom, Télécom ParisTech, CNRS LTCI, 75634 Paris, FranceInstitut Télécom, Télécom ParisTech, CNRS LTCI, 75634 Paris, FranceGiven a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process, and edges exist between two points if and only if their distance is less than a fixed given threshold. We compute explicitly the distribution of the number of connected components of this graph. The proof relies on inverting some Laplace transforms.http://dx.doi.org/10.1155/2011/350382 |
| spellingShingle | L. Decreusefond E. Ferraz On the One Dimensional Poisson Random Geometric Graph Journal of Probability and Statistics |
| title | On the One Dimensional Poisson Random Geometric Graph |
| title_full | On the One Dimensional Poisson Random Geometric Graph |
| title_fullStr | On the One Dimensional Poisson Random Geometric Graph |
| title_full_unstemmed | On the One Dimensional Poisson Random Geometric Graph |
| title_short | On the One Dimensional Poisson Random Geometric Graph |
| title_sort | on the one dimensional poisson random geometric graph |
| url | http://dx.doi.org/10.1155/2011/350382 |
| work_keys_str_mv | AT ldecreusefond ontheonedimensionalpoissonrandomgeometricgraph AT eferraz ontheonedimensionalpoissonrandomgeometricgraph |