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Bourgain's slicing problem and KLS isoperimetry up to polylog
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We prove that Bourgain's hyperplane conjecture and the Kannan-Lov\'asz-Simonovits (KLS) isoperimetric conjecture hold true up to a factor that is polylogarithmic in the dimension.
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Cited by 3 Pith papers
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Isomorphic Busemann--Petty for arbitrary measures: the sharp order
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Regularized Dikin Walks for Sampling Truncated Logconcave Measures, Mixed Isoperimetry and Beyond Worst-Case Analysis
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.
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Minimum Norm Interpolation via The Local Theory of Banach Spaces: The Role of Gaussianity
The sharp MSE bound for the ℓ1-minimum-norm interpolator under isotropic Gaussian covariates is recovered via the geometry of symmetric Gaussian polytopes, without the convex Gaussian min-max theorem.
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