Limit laws for the diameter of a random point set

Authors
Appel, Martin J. B. Najim, Christopher A. Russo, Ralph P.
Citation
B. Appel, Martin J. et al., Limit laws for the diameter of a random point set, Advances in applied probability , 34(1), 2002, pp. 1-10
Journal title
Advances in applied probability → ACNP
ISSN journal
00018678
Volume
34
Issue
1
Year of publication
2002
Pages
1 - 10
Database
ACNP
SICI code
Abstract
Let U1,U2,. be a sequence of i.i.d. random vectors distributed uniformly in a compact plane region A of unit area. Sufficient conditions on the geometry of A are provided under which the Euclidean diameter Dn of the first n of the points converges weakly upon suitable rescaling.