Any random vector in R^n dominated in convex order by a standard Gaussian is the sum of three standard Gaussians, solving Talagrand's convexity problem and a weak combinatorial analogue.
Lipschitz changes of variables via heat flow.arXiv preprint 2201.03403,
5 Pith papers cite this work. Polarity classification is still indexing.
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2026 5representative citing papers
Proves near-Lipschitz stability in 2-Wasserstein distance (up to log factor) and relative entropy stability for the Kim-Milman flow map w.r.t. target measure perturbations under regularity assumptions, with existence for finite second moment targets.
Sharp Lipschitz regularity for flow-matching vector fields and diffusion scores, with optimal time/dimension dependence, gives √d/N Wasserstein discretization error for Euler samplers and globally Lipschitz Gaussian-to-target transport maps implying Poincaré and log-Sobolev inequalities.
Constructs CD(1/2,∞) manifold on R² without Lipschitz transport from centered Gaussian and proves its weighted Laplacian eigenvalues are asymptotically negligible compared to the Gaussian case.
Establishes dimension- and step-optimal Wasserstein bounds for DDPMs under Lipschitz score conditions and broad variance schedules via Föllmer process analysis, recovering prior results and extending to log-concave targets.
citing papers explorer
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On Talagrand's Convexity Conjecture
Any random vector in R^n dominated in convex order by a standard Gaussian is the sum of three standard Gaussians, solving Talagrand's convexity problem and a weak combinatorial analogue.
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Near-Lipschitz stability of the Kim--Milman flow map
Proves near-Lipschitz stability in 2-Wasserstein distance (up to log factor) and relative entropy stability for the Kim-Milman flow map w.r.t. target measure perturbations under regularity assumptions, with existence for finite second moment targets.
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Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalities
Sharp Lipschitz regularity for flow-matching vector fields and diffusion scores, with optimal time/dimension dependence, gives √d/N Wasserstein discretization error for Euler samplers and globally Lipschitz Gaussian-to-target transport maps implying Poincaré and log-Sobolev inequalities.
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Geometric obstructions to Lipschitz transport between weighted Hessian $\mathrm{CD}(\kappa,\infty)$ manifolds
Constructs CD(1/2,∞) manifold on R² without Lipschitz transport from centered Gaussian and proves its weighted Laplacian eigenvalues are asymptotically negligible compared to the Gaussian case.
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Wasserstein bounds for denoising diffusion probabilistic models via the F\"ollmer process
Establishes dimension- and step-optimal Wasserstein bounds for DDPMs under Lipschitz score conditions and broad variance schedules via Föllmer process analysis, recovering prior results and extending to log-concave targets.