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

José Trashorras (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: Large deviations; $\infty$-wasserstein distance; minimax matching problem

Domaines: Probabilités [math.PR]

José Trashorras. Large Deviations for a matching problem related to the $\infty$-Wasserstein distance. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2018, 15, pp.247-278. ⟨hal-00641378v2⟩