Related papers: Bi-log-concavity: some properties and some remarks…

We establish sharp exponential deviation estimates of the information content as well as a sharp bound on the varentropy for the class of convex measures on Euclidean spaces. This generalizes a similar development for log-concave measures…

For sampling from a log-concave density, we study implicit integrators resulting from $\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the…

We compare weighted sums of i.i.d. positive random variables according to the usual stochastic order. The main inequalities are derived using majorization techniques under certain log-concavity assumptions. Specifically, let $Y_i$ be i.i.d.…

Caffarelli's contraction theorem bounds the derivative of the optimal transport map between a log-convex measure and a strongly log-concave measure. We show that an analogous phenomenon holds on the level of the trace: The trace of the…

The variation of a class of Orlicz moments with respect to the Asplund sum within the class of log-concave functions is demonstrated. Such a variational formula naturally leads to a family of dual Orlicz curvature measures for log-concave…

We prove that the Poisson distribution maximises entropy in the class of ultra-log-concave distributions, extending a result of Harremo\"{e}s. The proof uses ideas concerning log-concavity, and a semigroup action involving adding Poisson…

We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild…

A weighted relative isoperimetric inequality in convex cones is obtained via the Monge-Ampere equation. The method improves several inequalities in the literature, e.g. constants in a theorem of Cabre--Ros--Oton--Serra. Applications are…

This paper introduces an extension to the normal distribution through the polar method to capture bimodality and asymmetry, which are often observed characteristics of empirical data. The later two features are entirely controlled by a…

We consider the outstanding problem of sampling from an unnormalized density that may be non-log-concave and multimodal. To enhance the performance of simple Markov chain Monte Carlo (MCMC) methods, techniques of annealing type have been…

We analyze four different approaches to estimate a multivariate probability density (or the log-density) and its first and second order derivatives. Two methods, local log-likelihood and local Hyv\"arinen score estimation, are in terms of…

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…

This paper introduces and fully characterizes the novel class of quasi-logconvex measures of risk, to stand on equal footing with the rich class of quasi-convex measures of risk. Quasi-logconvex risk measures naturally generalize logconvex…

We report a recent developement on the theory of upper conical densities. More precicely, we look at what can be said in this respect for other measures than just the Hausdorff measure. We illustrate the methods involved by proving a result…

We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…

We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In…

This paper focuses on a challenging class of inverse problems that is often encountered in applications. The forward model is a complex non-linear black-box, potentially non-injective, whose outputs cover multiple decades in amplitude.…

We consider the free additive convolution semigroup $\lbrace \mu^{\boxplus t}:\,t\ge 1\rbrace$ and determine the local behavior of the density of $\mu^{\boxplus t}$ at the endpoints and at any singular point of its support. We then study…

The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme-value distribution may be approximated by the one of its extreme-value attractor. The extreme-value attractor has margins that belong to a…

A set in the Euclidean plane is said to be biconvex if, for some angle $\theta\in[0,\pi/2)$, all its sections along straight lines with inclination angles $\theta$ and $\theta+\pi/2$ are convex sets (i.e, empty sets or segments).…