Related papers: Order statistics and concentration of l_r norms fo…
We establish two-sided bounds for expectations of order statistics ($k$-th maxima) of moduli of coordinates of centered log-concave random vectors with uncorrelated coordinates. Our bounds are exact up to multiplicative universal constants…
We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the norms of projections of sums of independent…
We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entropy bounds for random variables satisfying a precise degree…
We establish uniform estimates for order statistics of sequences of independent identically distributed random variables with log-concave distribution in terms of Orlicz norms associated with the distribution function of the random…
An elementary proof is provided of sharp bounds for the varentropy of random vectors with log-concave densities, as well as for deviations of the information content from its mean. These bounds significantly improve on the bounds obtained…
We prove, using optimal transport tools, weighted Poincar'e inequalities for log-concave random vectors satisfying some centering conditions. We recover by this way similar results by Klartag and Barthe-Cordero-Erausquin for log-concave…
The Paouris inequality gives the large deviation estimate for Euclidean norms of log-concave vectors. We present a modified version of it and show how the new inequality may be applied to derive tail estimates of l_r-norms and suprema of…
We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration bounds. As an application, we derive concentration bounds for…
We derive new comparison inequalities between weak and strong moments of norms of random vectors with optimal (up to an universal factor) constants. We discuss applications to the concentration of log-concave random vectors and bounds on…
We derive two-sided bounds for moments of linear combinations of coordinates od unconditional log-concave vectors. We also investigate how well moments of such combinations may be approximated by moments of Gaussian random variables.
In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors.
We show sharpened forms of the concentration of measure phenomenon centered at first order stochastic expansions. The bound are based on second order difference operators and second order derivatives. Applications to functions on the…
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…
Log-concave distributions include some important distributions such as normal distribution, exponential distribution and so on. In this note, we show inequalities between two Lp-norms for log-concave distributions on the Euclidean space.…
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 study the log-concave measures, their characterization via the Pr\'ekopa-Leindler property and also define a subset of it whose elements are called super log-concave measures which have the property of satisfying a logarithmic Sobolev…
In recent years, log-concave density estimation via maximum likelihood estimation has emerged as a fascinating alternative to traditional nonparametric smoothing techniques, such as kernel density estimation, which require the choice of one…
It is well known that if a random vector satisfies a log-Sobolev inequality, all of its marginals have subgaussian tails. In the spirit of the KLS conjecture, we investigate whether this implication can be reversed under a log-concavity…
We obtain Rosenthal-type inequalities with sharp constants for moments of sums of independent random variables which are mixtures of a fixed distribution. We also identify extremisers in log-concave settings when the moments of summands are…
We prove estimates for $\mathbb{E} \| X: \ell_{p'}^n \to \ell_q^m\|$ for $p,q\ge 2$ and any random matrix $X$ having the entries of the form $a_{ij}Y_{ij}$, where $Y=(Y_{ij})_{1\le i\le m, 1\le j\le n}$ has i.i.d. isotropic log-concave…