A probability measure $\mu$ satisfies a $T_p$ transportation cost inequality with constant $c$ if $W_p(\mu, \nu)^2 \le 2c\,\mathrm{KL}(\nu \| \mu)$ for all $\nu \ll \mu$, where $W_p$ is the $p$-Wasserstein distance. For $p = 1$ ($T_1$), Bobkov–Götze 1999 showed this is *equivalent* to which concentration property?

Optimal Transport and Earth Mover's Distance

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A probability measure μ satisfies a T_{p} transportation cost inequality with constant c if W_{p} (μ, ν)^{2} \leq 2 c KL (ν ∥ μ) for all ν ≪ μ, where W_{p} is the p -Wasserstein distance. For p = 1 (T_{1}), Bobkov-Götze 1999 showed this is *equivalent* to which concentration property?