Related papers: A reverse Rogers-Shephard inequality for log-conca…
In this paper we study various Rogers-Shephard type inequalities for the lattice point enumerator $\mathrm{G}_{n}(\cdot)$ on $\mathbb{R}^n$. In particular, for any non-empty convex bounded sets $K,L\subset\mathbb{R}^n$, we show that…
We give an alternative proof of a recent result of Klartag on the existence of almost subgaussian linear functionals on convex bodies. If $K$ is a convex body in ${\mathbb R}^n$ with volume one and center of mass at the origin, there exists…
In this paper, we obtain some new inequalities for functions whose second derivatives' absolute value is s-convex and log-convex. Also, we give some applications for numerical integration.
We develop in this paper an amelioration of the method given by S. Bobkov and M. Ledoux in GAFA (2000). We prove by Prekopa-Leindler Theorem an optimal modified logarithmic Sobolev inequality adapted for all log-concave measure on $\dR^n$.…
We prove logarithmic Sobolev inequalities and concentration results for convex functions and a class of product random vectors. The results are used to derive tail and moment inequalities for chaos variables (in spirit of Talagrand and…
In this paper we further develop the theory of f-divergences for log-concave functions and their related inequalities. We establish Pinsker inequalities and new affine invariant entropy inequalities. We obtain new inequalities on functional…
We show that Shannon's entropy--power inequality admits a strengthened version in the case in which the densities are log-concave. In such a case, in fact, one can extend the Blachman--Stam argument to obtain a sharp inequality for the…
We introduce floating bodies for convex, not necessarily bounded subsets of $\mathbb{R}^n$. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of…
Using a discrete Bakry-{\'E}mery method based on the JKO scheme, relying on the dissipation of entropy and Fisher information along a discrete flow, we establish new generalized logarithmic Sobolev inequality for log-concave measures of the…
In this paper we consider some properties of the initial logarithmic coefficients for inverse functions of functions univalent in the unit disc. The case of convex functions is treated separately. We give estimate, in some cases sharp, 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 prove that the (B) conjecture and the Gardner-Zvavitch conjecture are true for all log-concave measures that are rotationally invariant, extending previous results known for Gaussian measures. Actually, our result apply beyond the case…
Stability version of the Prekopa-Leindler inequality for log-concave functions on the n-dimensional Euclidean space is established.
This is a continuation of our previous work 0712.4092. It is well known that various isoperimetric inequalities imply their functional ``counterparts'', but in general this is not an equivalence. We show that under certain convexity…
Proceeding the study of local properties of analytic functions started in [Br] we prove new dimensionless inequalities for such functions in terms of their Chebyshev degree. As a consequence, we obtain the reverse Holder inequalities for…
We investigate geometric and functional inequalities for the class of log-concave probability sequences. We prove dilation inequalities for log-concave probability measures on the integers. A functional analogue of this geometric inequality…
We prove an isoperimetric inequality for the uniform measure on a uniformly convex body and for a class of uniformly log-concave measures (that we introduce). These inequalities imply (up to universal constants) the log-Sobolev inequalities…
Weighted cone-volume functionals are introduced for the convex polytopes in $\mathbb{R}^n$. For these functionals, geometric inequalities are proved and the equality conditions are characterized. A variety of corollaries are derived,…
In this work we present a new, natural, definition for the mean width of log-concave functions. We show that the new definition coincide with a previous one by B. Klartag and V. Milman, and deduce some properties of the mean width,…
An inequality of Brascamp and Lieb provides a bound on the covariance of two functions with respect to log-concave measures. The bound estimates the covariance by the product of the $L^2$ norms of the gradients of the functions, where the…