Open Access
Translator Disclaimer
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 $X_1,\ldots,X_n,Y_1,\ldots,Y_n$ be i.i.d. with the uniform distribution on $(\lbrack 0,1\rbrack^2, \| \|)$, 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 $\inf_\pi \sum^n_{i=1} \exp\Bigg(\frac{\|X_i - Y_{\pi(i)}\|}{K(\log n/n)^{1/2}}\Bigg)^2,$ where $\pi$ ranges over all permutations of the integers $1,\ldots,n$, 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 $L_p$ transportation cost are also found.

Citation

Download Citation

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

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.3 • No. 4 • November, 1993
Back to Top