We study multivariate entire functions and polynomials with non-negative coefficients. A class of Strongly Log-Concave entire functions, generalizingMinkowski volume polynomials, is introduced: an entire function f in m variables is called Strongly Log-Concave if the function (∂x1) c1 ...(∂xm) mf is either zero or log((∂x1) c1 ...(∂xm) mf) is concave on R + . We start with yet another point of ...

We consider Cournot models of competition, where market participants choose the quantities they demand or supply. We study the loss of aggregate surplus due to the exercise of market power in Cournot competition, for both oligopsony and oligopoly models. We observe that efficiency loss is generally arbitrarily high in Cournot games, but also prove bounds on efficiency loss in several cases of i...

We prove a sharp inequality conjectured by Bobkov on the measure of dilations of Borel sets in the Euclidean space by a s-concave probability measure. Our result gives a common generalization of an inequality of Nazarov, Sodin and Volberg and a concentration inequality of Guédon. Applying our inequality to the level sets of functions satisfying a Remez type inequality, we deduce, as it is class...

Abstract John’s fundamental theorem characterizing the largest volume ellipsoid contained in a convex body $K$ $\mathbb{R}^{d}$ has seen several generalizations and extensions. One direction, initiated by V. Milman is to replace ellipsoids positions (affine images) of another $L$. Another, more recent direction consider logarithmically concave functions on instead bodies: we designate some spec...