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.
Bizeul,The slicing conjecture via small ball estimates, Ann
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abstract
Bourgain's slicing conjecture was recently resolved by Joseph Lehec and Bo'az Klartag. We present an alternative proof by establishing small ball probability estimates for isotropic log-concave measures. Our approach relies on the stochastic localization process and Guan's bound, techniques also used by Klartag and Lehec. The link between small ball probabilities and the slicing conjecture was first observed by Dafnis and Paouris and is established through Milman's theory of M-ellipsoids.
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2026 3representative citing papers
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