Journal article
Covering random points in a unit disk
Advances in applied probability, v 40(1), pp 22-30
Mar 2008
Abstract
Let D be the punctured unit disk. It is easy to see that no pair x, y in D can cover D in the sense that D cannot be contained in the union of the unit disks centred at x and y. With this fact in mind, let V
n
= {X
1, X
2, …, X
n
}, where X
1, X
2, … are random points sampled independently from a uniform distribution on D. We prove that, with asymptotic probability 1, there exist two points in V
n
that cover all of V
n
.
Metrics
Details
- Title
- Covering random points in a unit disk
- Creators
- Jennie C. Hansen - School of Mathematical & Computer SciencesEric Schmutz - Drexel UniversityLi Sheng - Drexel University
- Publication Details
- Advances in applied probability, v 40(1), pp 22-30
- Publisher
- Cambridge University Press
- Number of pages
- 9
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000255981300002
- Scopus ID
- 2-s2.0-44649153788
- Other Identifier
- 991019169643604721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Statistics & Probability