Large Deviations for a matching problem related to the $\infty$-Wasserstein distance
Résumé
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.
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