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Logarithmic bounds for isoperimetry and slices of convex sets

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arxiv 2303.14938 v2 pith:NL5T5657 submitted 2023-03-27 math.FA math.MGmath.PR

Bo'az Klartag This is my paper · ORCID
classification math.FAmath.MGmath.PR
keywords conjectureasz-simonovitsboundsbourgainconvexfactorholdimproved
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abstract

We prove that the Bourgain slicing conjecture and the Kannan-Lov\'asz-Simonovits (KLS) isoperimetric conjecture in $\mathbb{R}^n$ hold true up to a factor of $\sqrt{\log n}$. A new ingredient used in the proof is an improved log-concave Lichnerowicz inequality.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Regularized Dikin Walks for Sampling Truncated Logconcave Measures, Mixed Isoperimetry and Beyond Worst-Case Analysis

    cs.DS 2024-12 conditional novelty 7.0 of 10

    The soft-threshold Dikin walk mixes in O((m+kappa)n) iterations for truncated logconcave targets, supported by a new isoperimetric inequality combining Euclidean and Hilbert metrics.

  2. On the limit of random hives with GUE boundary conditions

    math.PR 2025-02 conditional novelty 6.0 of 10

    Scaled random hives with GUE boundary conditions converge in probability to a unique continuum hive whose value at a point v is the supremum of a functional over asymptotic height functions of lozenge tilings.

  3. The slicing conjecture via small ball estimates

    math.FA 2025-01 conditional novelty 5.0 of 10

    An alternative proof of the slicing conjecture is given through optimal small-ball estimates for isotropic log-concave vectors, using stochastic localization and Guan's bound.

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