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Functional inequalities along Wasserstein geodesics
We study functional inequalities along Wasserstein geodesics. If $μ$ 0 and $μ$ 1 are respectively $κ$ 0 -and $κ$ 1 -strongly log-concave probability measures on R n , we prove that their quadratic Wasserstein geodesic satisfies for all probability measures $ν$ on R n . The coefficient is sharp. By
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