Related papers: Concentration Inequalities for Ultra Log-Concave D…

We prove sharp anti-concentration results for log-concave random variables on the real line in both the discrete and continuous setting. Our approach is elementary and uses majorization techniques to recover and extend some recent and not…

We propose a new discretization of the mirror-Langevin diffusion and give a crisp proof of its convergence. Our analysis uses relative convexity/smoothness and self-concordance, ideas which originated in convex optimization, together with a…

This paper contains a thorough investigation of invariant distributions supported on limit sets of discrete groups acting convex cocompactly on symmetric spaces of negative curvature. It can be considered as a continuation of…

We prove a log-Sobolev inequality for a certain class of log-concave measures in high dimension. These are the probability measures supported on the unit cube in R^n whose density takes the form exp(-H) where the function H is assumed to be…

In this paper, we use the semi-group method and an adaptation of the $L^2-$method of H\"ormander to establish some $\Phi-$entropy inequalities and asymmetric covariance estimates for the strictly convex measures in $\mathbb R^n$. These…

We consider the problem of lower bounding a generalized Minkowski measure of subsets of a convex body with a log-concave probability measure, conditioned on the set size. A bound is given in terms of diameter and set size, which is sharp…

In this paper, we study two problems: (1) estimation of a $d$-dimensional log-concave distribution and (2) bounded multivariate convex regression with random design with an underlying log-concave density or a compactly supported…

Maximum likelihood estimation of a log-concave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannon entropy problem. Closely related maximum…

We provide a sharp rate of convergence in the central limit theorem for random vectors with an unconditional, log-concave density. The argument relies on analysis of the Neumann laplacian on convex domains and on the theory of optimal…

We present concentration inequalities on the multislice which are based on (modified) log-Sobolev inequalities. This includes bounds for convex functions and multilinear polynomials. As an application we show concentration results for the…

We investigate a convexity properties for normalized log moment generating function continuing a recent investigation of Chen of convex images of Gaussians. We show that any variable satisfying a ``Ehrhard-like'' property for its…

In Statistics, log-concave density estimation is a central problem within the field of nonparametric inference under shape constraints. Despite great progress in recent years on the statistical theory of the canonical estimator, namely the…

We prove higher order concentration bounds for functions on Stiefel and Grassmann manifolds equipped with the uniform distribution. This partially extends previous work for functions on the unit sphere. Technically, our results are based on…

We improve known upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings. Some of our bounds are sharp up to logarithmic factors.

W. Schmidt, H. Montgomery, and J. Beck proved a result on irregularities of distribution with respect to $d$-dimensional balls. In this paper, we extend their result to any $d$-dimensional convex body with a smooth boundary and finite order…

We prove that for $s<0$, $s$-concave measures on ${\mathbb R}^n$ satisfy a thin shell concentration similar to the log-concave one. It leads to a Berry-Esseen type estimate for their one dimensional marginal distributions. We also establish…

We investigate new convex relaxations for the pooling problem, a classic nonconvex production planning problem in which input materials are mixed in intermediate pools, with the outputs of these pools further mixed to make output products…

We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of expectation of the supremum of "symmetric exponential" processes compared to the Gaussian ones in…

We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions…

In the nice recent work [48], S. Wang established uniform log-Sobolev inequalities for mean field particles when the energy is flat convex. In this note we comment how to extend his proof to some semi-convex energies provided the curvature…