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Large Deviations for a matching problem related to the ∞-Wasserstein distance

Trashorras, José (2011), Large Deviations for a matching problem related to the ∞-Wasserstein distance. https://basepub.dauphine.fr/handle/123456789/7529

Type
Document de travail / Working paper
External document link
http://hal.archives-ouvertes.fr/hal-00641378/fr/
Date
2011
Publisher
Université Paris-Dauphine
Published in
Paris
Pages
21
Metadata
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Author(s)
Trashorras, José
Abstract (EN)
Let $(E,d)$ be a compact metric space, $X=(X_1,\dots,X_n,\dots)$ and $Y=(Y_1,\dots,Y_n,\dots)$ two independent sequences of independent $E$-valued random variables and $(L^X_n)_{n \geq 1}$ and $(L^Y_n)_{n \geq 1}$ the associated sequences of empirical measures. We establish a Large Deviations Principle for $(W_{\infty}(L^X_n,L^Y_n))_{n \geq 1}$ where $W_{\infty}$ is the $\infty$-Wasserstein distance.
Subjects / Keywords
minimax matching problem; infinity - wasserstein distance; Large deviations