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· 2026 · Advances in Mathematics · DOI 10.1016/j.aim.2026.110841 · arXiv 2026.110841

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Sharp Poincar\'e Interpolation Along Wasserstein Geodesics

math.PR · 2026-07-12 · accept · novelty 7.0

Along the Wasserstein geodesic between κi-strongly log-concave measures, the Poincaré constant of μt satisfies √CP(μt) ≤ (1−t)/√κ0 + t/√κ1, with equality iff both endpoints share a curvature-saturating Gaussian factor.

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  • Sharp Poincar\'e Interpolation Along Wasserstein Geodesics math.PR · 2026-07-12 · accept · none · ref 3

    Along the Wasserstein geodesic between κi-strongly log-concave measures, the Poincaré constant of μt satisfies √CP(μt) ≤ (1−t)/√κ0 + t/√κ1, with equality iff both endpoints share a curvature-saturating Gaussian factor.