Nearly-tight O(sqrt(d)) approximation for zonotope containment in the oracle model, with a proof of Talagrand's conjecture for constant Delta-modular zonotopes and a tight Theta(d/log d) bound for general convex bodies.
A note on Bourgain’s slicing problem
4 Pith papers cite this work. Polarity classification is still indexing.
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2026 4representative citing papers
Random normed spaces from isotropic log-concave measures satisfy d_BM >= cn / ln(1+m/n) with high probability, sharp in both parameters and recovering the order-n extremal when m is linear in n.
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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Nearly-Tight Bounds for Zonotope Containment and Beyond
Nearly-tight O(sqrt(d)) approximation for zonotope containment in the oracle model, with a proof of Talagrand's conjecture for constant Delta-modular zonotopes and a tight Theta(d/log d) bound for general convex bodies.
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Banach-Mazur distances and basis constants of isotropic log-concave random spaces
Random normed spaces from isotropic log-concave measures satisfy d_BM >= cn / ln(1+m/n) with high probability, sharp in both parameters and recovering the order-n extremal when m is linear in n.
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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.
- Functional perimeter and the dimensional Brunn-Minkowski inequality for log-concave measures