On the clustering of independent uniform random variables

Authors:
Sándor Csörgő;Wei Biao Wu
Affiliations:
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged, 6720, Hungary;Department of Statistics, University of Chicago, 5734 University Avenue, Chicago, Illinois 60637
Venue:
Random Structures & Algorithms
Year:
2004

Citing 1
Cited 1

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Abstract

We consider the number Kn of clusters at a distance level dn ∈ (0, 1) of n independent random variables uniformly distributed in [0, 1], or the number Kn of connected components in the random interval graph generated by these variables and dn, and, depending upon how fast dn → 0 as n → ∞, determine the asymptotic distribution of Kn, with rates of convergence, and of related random variables that describe the cluster sizes. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004