Steinhaus's geometric location problem for random samples in the plane
- 1 March 1982
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 14 (1) , 56-67
- https://doi.org/10.2307/1426733
Abstract
Let whereXi, 1 ≦i≦n, are i.i.d. and uniformly distributed in [0, 1]2. It is proved thatMn∽cn1–p/2a.s. for 1 ≦p<2. This result is motivated by recent developments in the theory of algorithms and the theory of subadditive processes as well as by a well-known problem of H. Steinhaus.Keywords
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