Related papers: Preservation of log-concavity on summation
In this paper, we provide criteria for the log-concavity of rows and the strong $q$-log-convexity of the generating functions of rows in more generalized triangles. Additionally, we prove that the bi$^s$nomial transformation not only…
We establish two-weight norm inequalities for singular integral operators defined on spaces of homogeneous type. We do so first when the weights satisfy a double bump condition and then when the weights satisfy separated logarithmic bump…
We construct infinite families of trees whose independence polynomials violate log-concavity at an arbitrary number of indices. This affirmatively answers a question of D. Galvin.
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…
We consider convex hulls of random walks whose steps belong to the domain of attraction of a stable law in $\mathbb{R}^d$. We prove convergence of the convex hull in the space of all convex and compact subsets of $\mathbb{R}^d$, equipped…
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…
It is well known that a random vector with given marginal distributions is comonotonic if and only if it has the largest sum with respect to the convex order [ Kaas, Dhaene, Vyncke, Goovaerts, Denuit (2002), A simple geometric proof that…
Existence of mass-conserving self-similar solutions with a sufficiently small total mass is proved for a specific class of homogeneous coagulation and fragmentation coefficients. The proof combines a dynamical approach to construct such…
It has been widely acknowledged that probabilistic independence and logical independence cannot be coherently reconciled. By bridging these two notions, this paper addresses three long-standing problems that have puzzled the field of…
We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference…
Let $(M,\omega)$ be a closed $2n$-dimensional semifree Hamiltonian $S^1$-manifold with only isolated fixed points. We prove that a density function of the Duistermaat-Heckman measure is log-concave. Moreover, we prove that $(M,\omega)$ and…
We prove a logarithmic convexity result for exponentially weighted $L^2$-norms of solutions to electromagnetic Schr\"odinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique…
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by infinitely divisible laws may be transferred to the estimation of the closeness of…
We expand upon the notion of equivariant log concavity, and make equivariant log concavity conjectures for Orlik--Solomon algebras of matroids, Cordovil algebras of oriented matroids, and Orlik--Terao algebras of hyperplane arrangements. In…
We consider testing whether a set of Gaussian variables, selected from the data, is independent of the remaining variables. We assume that this set is selected via a very simple approach that is commonly used across scientific disciplines:…
We prove stability estimates for the Shannon-Stam inequality (also known as the entropy-power inequality) for log-concave random vectors in terms of entropy and transportation distance. In particular, we give the first stability estimate…
It is known that the $S(n,k)$ Stirling numbers as well as the ordered Stirling numbers $k!S(n,k)$ form log-concave sequences. Although in the first case there are many estimations about the mode, for the ordered Stirling numbers such…
In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was…
We study the singular series associated to a cubic form with integer coefficients. If the number of variables is at least $10$, we prove the absolute convergence (and hence positivity) under the assumption of Davenport's Geometric…
The contents are divided into two papers "The Monotone Cumulants" (arXiv:0907.4896) and "Conditionally monotone independence" (arXiv:0907.5473).