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August, 1993 A Matching Problem and Subadditive Euclidean Functionals
WanSoo T. Rhee
Ann. Appl. Probab. 3(3): 794-801 (August, 1993). DOI: 10.1214/aoap/1177005364


A classical paper by Steele establishes a limit theorem for a wide class of random processes that arise in problems of geometric probability. We propose a different (and arguably more general) set of conditions under which complete convergence holds. As an application of our framework, we prove complete convergence of $M(X_1, \ldots, X_n)/\sqrt n$, where $M(X_1, \ldots, X_n)$ denotes the shortest sum of the lengths of $\lfloor n/2\rfloor$ segments that match $\lfloor n/2\rfloor$ disjoint pairs of points among $X_1, \ldots, X_n$, where the random variables $X_1, \ldots, X_n, \ldots$ are independent and uniformly distributed in the unit square.


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WanSoo T. Rhee. "A Matching Problem and Subadditive Euclidean Functionals." Ann. Appl. Probab. 3 (3) 794 - 801, August, 1993.


Published: August, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0784.60020
MathSciNet: MR1233626
Digital Object Identifier: 10.1214/aoap/1177005364

Primary: 60D05
Secondary: 60G17

Keywords: complete convergence , Matching problem , subadditive functionals

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.3 • No. 3 • August, 1993
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