Open Access
November, 1993 The Integrability of the Square Exponential Transportation Cost
M. Talagrand, J. E. Yukich
Ann. Appl. Probab. 3(4): 1100-1111 (November, 1993). DOI: 10.1214/aoap/1177005274

Abstract

Let X1,,Xn,Y1,,Yn be i.i.d. with the uniform distribution on ([0,1]2,), where denotes the Euclidean norm. Using a new presentation of the Ajtai-Komlos-Tusnady (AKT) transportation algorithm, it is shown that the square exponential transportation cost infπi=1nexp(XiYπ(i)K(logn/n)1/2)2, where π ranges over all permutations of the integers 1,,n, satisfies an integrability condition. This condition strengthens the optimal matching results of AKT and supports a recent conjecture of Talagrand. Rates of growth for the Lp transportation cost are also found.

Citation

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M. Talagrand. J. E. Yukich. "The Integrability of the Square Exponential Transportation Cost." Ann. Appl. Probab. 3 (4) 1100 - 1111, November, 1993. https://doi.org/10.1214/aoap/1177005274

Information

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

zbMATH: 0784.60014
MathSciNet: MR1241036
Digital Object Identifier: 10.1214/aoap/1177005274

Subjects:
Primary: 05C70
Secondary: 60C05 , 60D05

Keywords: Euclidean bipartite matching , subgaussian , transportation cost

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.3 • No. 4 • November, 1993
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