Divergence for \(s\)-concave and log concave functions

DOI10.1016/j.aim.2014.02.013zbMath1310.26016arXiv1307.5409OpenAlexW2038387772MaRDI QIDQ2445852

Elisabeth M. Werner, Umut Caglar

Publication date: 15 April 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.5409

zbMATH Keywords

entropydivergenceaffine isoperimetric inequalitieslog Sobolev inequalities

Mathematics Subject Classification ID

Convex functions and convex programs in convex geometry (52A41) Inequalities and extremum problems involving convexity in convex geometry (52A40) Inequalities involving other types of functions (26D07)

Related Items

LYZ ellipsoid and Petty projection body for log-concave functions, The spherical convex floating body, Constrained convex bodies with extremal affine surface areas, Curvature functionals on convex bodies, Floating functions, Projection body and isoperimetric inequalities for \(s\)-concave functions, Functional geominimal surface area and its related affine isoperimetric inequality, On mixed quermassintegral for log-concave functions, The mixed L_p affine surface areas for functions, Approximation of smooth convex bodies by random polytopes, Mixedf-divergence and inequalities for log-concave functions, A Steiner formula in the \(L_p\) Brunn Minkowski theory, Flag numbers and floating bodies, Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory, Ulam floating bodies, Orlicz Addition for Measures and an Optimization Problem for the -divergence, Best approximation of functions by log-polynomials, The functional inequality for the mixed quermassintegral, Pinsker inequalities and related Monge-Ampere equations for log-concave functions, Geometry of log-concave functions: the \(L_p\) Asplund sum and the \(L_p\) Minkowski problem, Affine invariant maps for log-concave functions

Cites Work

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• Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality
• Rényi divergence and \(L_p\)-affine surface area for convex bodies
• Minkowski areas and valuations
• Hermitian integral geometry
• Invariant valuations on star-shaped sets
• Inequalities for mixed \(p\)-affine surface area
• General affine surface areas
• Crofton measures and Minkowski valuations
• A direct proof of the functional Santaló inequality
• General \(L_{p}\) affine isoperimetric inequalities
• Continuous rotation invariant valuations on convex sets
• Variance inequalities for functions of Gaussian variables
• Blaschke-Santaló inequalities
• Ellipsoids and matrix-valued valuations
• On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
• On the \(p\)-affine surface area
• A new ellipsoid associated with convex bodies
• The discrete planar \(L_0\)-Minkowski problem
• Sharp affine \(L_ p\) Sobolev inequalities.
• Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations.
• Intersection bodies and the Busemann-Petty inequalities in \(\mathbb{R}^ 4\)
• The Cramer-Rao inequality for star bodies
• Projection bodies and valuations
• Surface bodies and \(p\)-affine surface area
• Moment-entropy inequalities.
• A new class of metric divergences on probability spaces and its applicability in statistics
• Generalizations of the Busemann-Petty problem for sections of convex bodies
• Covariance identities and inequalities for functionals on Wiener and Poisson spaces
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Curvature relations and affine surface area for a general convex body and its polar
• Star valuations and dual mixed volumes
• A characterization of affine surface area
• Convex set functions in \(d\)-space
• Some functional forms of Blaschke-Santaló inequality
• New \(L_p\) affine isoperimetric inequalities
• The dual Brunn-Minkowski theory for bounded Borel sets: dual affine quermassintegrals and inequalities
• Volume inequalities for subspaces of \(L_p\)
• On the Blaschke-Santaló inequality
• Über die Finsler-Räume mit \(A_i=0\)
• Functional Versions ofL_p-Affine Surface Area and Entropy Inequalities
• Blaschke valuations
• Relative entropy of cone measures and L _p centroid bodies
• Intersection bodies and valuations
• CramÉr–Rao and Moment-Entropy Inequalities for Renyi Entropy and Generalized Fisher Information
• On Divergences and Informations in Statistics and Information Theory
• Convolutions, Transforms, and Convex Bodies
• The convex floating body.
• Information theoretic inequalities
• Distribution estimation consistent in total variation and in two types of information divergence
• The Santaló-regions of a convex body
• Affine inequalities and radial mean bodies
• Inequalities between entropy and index of coincidence derived from information diagrams
• Mixed ƒ-divergence for Multiple Pairs of Measures
• Information, Divergence and Risk for Binary Experiments
• Relative entropies for convex bodies
• On $L_p$-affine surface areas
• The Santaló point of a function, and a functional form of the Santaló inequality
• Elements of Information Theory
• Markov Processes and the H-Theorem
• Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture