Related papers: A reverse entropy power inequality for log-concave…

Industrial and power systems rely on engineering predictions of the flow properties of working fluids. The paper proposes a way of the utilization of the vapor quality values along the new retrograde condensation curve in the generation of…

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…

Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for…

In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and the volume of…

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…

We extend the notion of John's ellipsoid to the setting of integrable log-concave functions. This will allow us to define the integral ratio of a log-concave function, which will extend the notion of volume ratio, and we will find the…

Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state…

In this article, we study the stability in the inverse problem of determining the time-dependent convection term and density coefficient appearing in the convection-diffusion equation, from partial boundary measurements. For dimension…

The region of entropic vectors is a convex cone that has been shown to be at the core of many fundamental limits for problems in multiterminal data compression, network coding, and multimedia transmission. This cone has been shown to be…

We establish upper bounds for tails of order statistics of isotropic log-concave vectors and apply them to derive a concentration of l_r norms of such vectors.

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

We consider the problem of causal inference based on observational data (or the related missing data problem) with a binary or discrete treatment variable. In that context, we study inference for the counterfactual density functions and…

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 introduce the volume entropy semi-norm in real homology and show that it satisfies functorial properties similar to the ones of the simplicial volume. Answering a question of M. Gromov, we prove that the volume entropy semi-norm is…

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…

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…

In this paper, we provide explicit lower bounds with respect to some quantities of interest (parameters of the underlying distribution, dimension, geometrical characteristics of the domain, position of the origin, etc.) on the spectral gap…

In this paper, we give some $l_p$-type inequalities about sequences satisfying certain quasi monotone type properties. As special cases, reverse $l_p$-type inequalities for non-negative decreasing sequences are obtained. The inequalities…

We extend the result of Ball and Nguyen on the jump of entropy under convolution for logconcave random vectors. We show that the result holds for any pair of vectors (not necessarily identically distributed) and that a similar inequality…

We study the convergence of states under continuous-time depolarizing channels with full rank fixed points in terms of the relative entropy. The optimal exponent of an upper bound on the relative entropy in this case is given by the…