Bourgain's slicing problem and KLS isoperimetry up to polylog
From MaRDI portal
Publication:2088129
DOI10.1007/s00039-022-00612-9OpenAlexW4285545993MaRDI QIDQ2088129
Publication date: 21 October 2022
Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2203.15551
Probability measures on topological spaces (60B05) Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)
Related Items (13)
Self-improvement of the Bakry-Emery criterion for Poincaré inequalities and Wasserstein contraction using variable curvature bounds ⋮ A note on the reduction of the slicing problem to centrally symmetric convex bodies ⋮ On a multi-integral norm defined by weighted sums of log-concave random vectors ⋮ Comparison problems for Radon transforms ⋮ Long lines in subsets of large measure in high dimension ⋮ Tyler's and Maronna's M-estimators: non-asymptotic concentration results ⋮ Unnamed Item ⋮ A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures ⋮ The Langevin Monte Carlo algorithm in the non-smooth log-concave case ⋮ Half-space depth of log-concave probability measures ⋮ Stability of the isodiametric problem on the sphere and in the hyperbolic space ⋮ Covariance representations, \(L^p\)-Poincaré inequalities, Stein's kernels, and high-dimensional CLTs ⋮ Threshold for the expected measure of random polytopes
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Interpolating thin-shell and sharp large-deviation estimates for isotropic log-concave measures
- A Berry-Esseen type inequality for convex bodies with an unconditional basis
- Concentration of mass on convex bodies
- On convex perturbations with a bounded isotropic constant
- Power-law estimates for the central limit theorem for convex sets
- Concentration in a thin Euclidean shell for log-concave measures
- Isoperimetric and analytic inequalities for log-concave probability measures
- The (B) conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems
- Isoperimetric problems for convex bodies and a localization lemma
- An almost constant lower bound of the isoperimetric coefficient in the KLS conjecture
- Asymptotics of graphical projection pursuit
- Thin shell implies spectral gap up to polylog via a stochastic localization scheme
- A central limit theorem for convex sets
- Approximately gaussian marginals and the hyperplane conjecture
- On High Dimensional Maximal Functions Associated to Convex Bodies
- Logarithmically concave functions and sections of convex sets in $R^{n}$
- A note on the isoperimetric constant
- The central limit problem for convex bodies
- Analysis and Geometry of Markov Diffusion Operators
- Spectral gaps, symmetries and log-concave perturbations
- A Generalized Central Limit Conjecture for Convex Bodies
- <scp>Log‐Sobolev</scp> Inequality for the Continuum <scp>Sine‐Gordon</scp> Model
- Stochastic localization + Stieltjes barrier = tight bound for log-Sobolev
- Bounding the Norm of a Log-Concave Vector Via Thin-Shell Estimates
- Monotonicity properties of optimal transportation and the FKG and related inequalities
This page was built for publication: Bourgain's slicing problem and KLS isoperimetry up to polylog
