Concentration of mass on convex bodies
From MaRDI portal
Publication:866875
DOI10.1007/s00039-006-0584-5zbMath1114.52004OpenAlexW2077458243WikidataQ56221698 ScholiaQ56221698MaRDI QIDQ866875
Publication date: 14 February 2007
Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00039-006-0584-5
Local theory of Banach spaces (46B07) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)
Related Items (only showing first 100 items - show all)
Condition number of a square matrix with i.i.d. columns drawn from a convex body ⋮ The \(L_{p}\)-Minkowski problem for \(-n < p < 1\) ⋮ An isomorphic Dvoretzky-Milman theorem using general random ensembles ⋮ On the interval of fluctuation of the singular values of random matrices ⋮ Sampling discretization and related problems ⋮ A Berry-Esseen type inequality for convex bodies with an unconditional basis ⋮ The curse of dimensionality for numerical integration on general domains ⋮ ON THE EXISTENCE OF SUPERGAUSSIAN DIRECTIONS ON CONVEX BODIES ⋮ Concentration phenomena in high dimensional geometry ⋮ A stability result for mean width of \(L_{p}\)-centroid bodies ⋮ Rogers-Shephard inequality for log-concave functions ⋮ Uniform cover inequalities for the volume of coordinate sections and projections of convex bodies ⋮ Thin-shell concentration for convex measures ⋮ The LYZ centroid conjecture for star bodies ⋮ Circular law for sparse random regular digraphs ⋮ Empirical processes with a bounded \(\psi_1\) diameter ⋮ The minimal Orlicz surface area ⋮ Orlicz-Lorentz centroid bodies ⋮ On determinants and the volume of random polytopes in isotropic convex bodies ⋮ Covariance estimation for distributions with \({2+\varepsilon}\) moments ⋮ Power-law estimates for the central limit theorem for convex sets ⋮ On the thin-shell conjecture for the Schatten classes ⋮ Quantum ergodicity of random orthonormal bases of spaces of high dimension ⋮ On the convergence of the extremal eigenvalues of empirical covariance matrices with dependence ⋮ Constrained convex bodies with extremal affine surface areas ⋮ \(\ell _{1}\)-regularized linear regression: persistence and oracle inequalities ⋮ Approximations of convex bodies by measure-generated sets ⋮ Affine invariant points ⋮ On the isoperimetric constant, covariance inequalities and \(L_{p}\)-Poincaré inequalities in dimension one ⋮ The Orlicz-Lorentz centroid inequality for star bodies* ⋮ Orlicz-John ellipsoids ⋮ The Brunn-Minkowski-Firey inequality for nonconvex sets ⋮ The Orlicz centroid inequality for star bodies ⋮ Sharp bounds on the rate of convergence of the empirical covariance matrix ⋮ On generic chaining and the smallest singular value of random matrices with heavy tails ⋮ Hyperplane sections of convex bodies ⋮ COMPARISON OF WEAK AND STRONG MOMENTS FOR VECTORS WITH INDEPENDENT COORDINATES ⋮ Restricted isometry property of matrices with independent columns and neighborly polytopes by random sampling ⋮ Convex geometry and its applications. Abstracts from the workshop held December 12--18, 2021 (hybrid meeting) ⋮ A probabilistic take on isoperimetric-type inequalities ⋮ Quermaßintegrals and asymptotic shape of random polytopes in an isotropic convex body ⋮ Geometry of log-concave ensembles of random matrices and approximate reconstruction ⋮ Estimating support functions of random polytopes via Orlicz norms ⋮ The CLT in high dimensions: quantitative bounds via martingale embedding ⋮ On the Orlicz Minkowski problem for polytopes ⋮ Hadamard products and moments of random vectors ⋮ Isomorphic properties of intersection bodies ⋮ Bounds on optimal transport maps onto log-concave measures ⋮ The log-Brunn-Minkowski inequality ⋮ Neighborhoods on the Grassmannian of marginals with bounded isotropic constant ⋮ Anisotropic fractional Sobolev norms ⋮ Asymmetric anisotropic fractional Sobolev norms ⋮ Centroid bodies and the logarithmic Laplace transform - A unified approach ⋮ Random doubly stochastic matrices: the circular law ⋮ Estimates for the affine and dual affine quermassintegrals of convex bodies ⋮ Interpolating thin-shell and sharp large-deviation estimates for isotropic log-concave measures ⋮ A central limit theorem for convex sets ⋮ A remark on the slicing problem ⋮ \(\mathrm{SL}(n)\) contravariant \(L_p\) harmonic valuations on polytopes ⋮ On the isotropic constant of random polytopes with vertices on an \(\ell_p\)-sphere ⋮ On the geometry of random convex sets between polytopes and zonotopes ⋮ On weakly bounded empirical processes ⋮ Random approximation and the vertex index of convex bodies ⋮ The logarithmic Minkowski problem for polytopes ⋮ BRUNN–MINKOWSKI TYPE INEQUALITIES FOR Lp MOMENT BODIES ⋮ The logarithmic Minkowski problem ⋮ Order statistics and concentration of \(l_r\) norms for log-concave vectors ⋮ Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles ⋮ Heat flow and quantitative differentiation ⋮ On the volume of caps and bounding the mean-width of an isotropic convex body ⋮ Small ball probability estimates, \(\psi_2\)-behavior and the hyperplane conjecture ⋮ Concentration in a thin Euclidean shell for log-concave measures ⋮ How close is the sample covariance matrix to the actual covariance matrix? ⋮ The even Orlicz Minkowski problem ⋮ Between Paouris concentration inequality and variance conjecture ⋮ Approximating the moments of marginals of high-dimensional distributions ⋮ Spectral norm of products of random and deterministic matrices ⋮ Remarks on an inequality of Rogers and Shephard ⋮ On the convex infimum convolution inequality with optimal cost function ⋮ An almost constant lower bound of the isoperimetric coefficient in the KLS conjecture ⋮ Estimation in High Dimensions: A Geometric Perspective ⋮ Asymptotic shape of a random polytope in a convex body ⋮ A note on volume thresholds for random polytopes ⋮ Approximating \(L_p\) unit balls via random sampling ⋮ Non-asymptotic results for singular values of Gaussian matrix products ⋮ Weak and strong moments of ℓᵣ-norms of log-concave vectors ⋮ On Gaussian marginals of uniformly convex bodies ⋮ Smoothness in the \(L_p\) Minkowski problem for \(p<1\) ⋮ On \(\mathcal{Z}_p\)-norms of random vectors ⋮ An asymptotic thin shell condition and large deviations for random multidimensional projections ⋮ High dimensional random sections of isotropic convex bodies ⋮ Affine quermassintegrals of random polytopes ⋮ On mixed \(L_{p}\) John ellipsoids ⋮ Orlicz projection bodies ⋮ Bourgain's slicing problem and KLS isoperimetry up to polylog ⋮ THE SPECTRUM OF RANDOM KERNEL MATRICES: UNIVERSALITY RESULTS FOR ROUGH AND VARYING KERNELS ⋮ The \(L_p\) Minkowski problem for polytopes for \(0 < p < 1\) ⋮ Asymptotic shape of the convex hull of isotropic log-concave random vectors ⋮ On the intersection of random rotations of a symmetric convex body ⋮ The planar \(L_{p}\)-Minkowski problem for \(0<p<1\)
This page was built for publication: Concentration of mass on convex bodies
