Related papers: New characterizations of log-concavity

We prove log-concavity of the lengths of the top rows of Young diagrams under Poissonized Plancherel measure. This is the first known positive result towards a 2008 conjecture of Chen that the length of the top row of a Young diagram under…

In this paper, we use the analytic method of Odlyzko and Richmond to study the log-concavity of power series. If $f(z) = \sum_n a_nz^n$ is an infinite series with $a_n \geq 1$ and $a_0 + \cdots + a_n = O(n + 1)$ for all $n$, we prove that a…

We characterize the topological non-cancellative cones that are expressible as projective limits of finite powers of $[0,\infty]$. These are also the cones of lower semicontinuous extended-valued traces on AF C*-algebras. Our main result…

In this note we study a positivity notion for the curvature of the Bismut connection; more precisely, we study the notion of \emph{Bismut-Griffiths-positivity} for complex Hermitian non-K\"ahler manifolds. Since the K\"ahler-Ricci flow…

Let X be a normal variety such that $K_X$ is Q-Cartier, and let $f: X \rightarrow X$ be a finite surjective morphism of degree at least two. We establish a close relation between the irreducible components of the locus of singularities that…

In this paper we extend of the notion of algebraically closed given in the case of groups and skew fields to an arbitrary h-inductive theory. The main subject of this paper is the study of the notion of positive algebraic closedness and its…

It is well-known that measures whose density is the form $e^{-V}$ where $V$ is a uniformly convex potential on $\RR^n$ attain strong concentration properties. In search of a notion of log-concavity on the discrete hypercube, we consider…

In this note, we introduce a new curvature condition called the $2-$positive bisectional curvature on compact K\"{a}hler manifolds. We then deduce a characterization theorem for manifolds with $2-$positive bisectional curvature, which can…

Horizontal and vertical generating functions and recursion relations have been investigated by Comtet for triangular double sequences. In this paper we investigate the horizontal and vertical log-concavity of triangular sequences assigned…

Using calculus we show how to prove some combinatorial inequalities of the type log-concavity or log-convexity. It is shown by this method that binomial coefficients and Stirling numbers of the first and second kinds are log-concave, and…

John's inclusion states that a convex body in $\mathbb{R}^d$ can be covered by the $d$-dilation of its maximal volume ellipsoid. We obtain a certain John-type inclusion for log-concave functions. As a byproduct of our approach, we establish…

The eventual concavity properties are useful to characterize geometric properties of the final state of solutions to parabolic equations. In this paper we give characterizations of the eventual concavity properties of the heat flow for…

This paper revisits the modeling of multicomponent diffusion within the framework of thermodynamics of irreversible processes. We briefly review the two well-known main approaches, leading to the generalized Fick-Onsager multicomponent…

We develop a new method for proving that a flow has the so-called strong convolution singularity property, i.e. the Gaussian system induced by its (reduced) maximal spectral type has simple spectrum. We use these methods to give examples of…

Empirical observations show that turbulence exhibits a broad range of scaling exponents, characterizing how the velocity gradients diverge in the inviscid limit. These exponents are thought to be linked to singular solutions of the Euler…

Real-stable, Lorentzian, and log-concave polynomials are well-studied classes of polynomials, and have been powerful tools in resolving several conjectures. We show that the problems of deciding whether a polynomial of fixed degree is real…

Let v be a multiplicative arithmetic function with support of positive asymptotic density. We prove that for any not identically zero arithmetic function f such that \sum_{f(n) \neq 0} 1 / n < \infty, the support of the Dirichlet…

We develop the basic model theory of local positive logic, a new logic that mixes positive logic (where negation is not allowed) and local logic (where models omit types of infinite distant pairs). We study several basic model theoretic…

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…

We prove a lemma, which we call the Order Ideal Lemma, that can be used to demonstrate a wide array of log-concavity and log-convexity results in a combinatorial manner using order ideals in distributive lattices. We use the Order Ideal…