Related papers: A strong log-concavity property for measures on Bo…
Menon's proof of the preservation of log-concavity of sequences under convolution becomes simpler when adapted to 2-sided infinite sequences. Under assumption of log-concavity of two 2-sided infinite sequences, the existence of the…
Bi-log-concavity of probability measures is a univariate extension of the notion of log-concavity that has been recently proposed in a statistical literature. Among other things, it has the nice property from a modelisation perspective to…
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 give counterexamples and a few positive results related to several conjectures of R. Pemantle and D. Wagner concerning negative correlation and log-concavity properties for probability measures and relations between them. Most of the…
We prove that the (B) conjecture and the Gardner-Zvavitch conjecture are true for all log-concave measures that are rotationally invariant, extending previous results known for Gaussian measures. Actually, our result apply beyond the case…
We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure.
We review and formulate results concerning log-concavity and strong-log-concavity in both discrete and continuous settings. We show how preservation of log-concavity and strongly log-concavity on $\mathbb{R}$ under convolution follows from…
Let $\mu$ and $\nu$ be two probability measures on $\R^d$, where $\mu(\d x)= \e^{-V(x)}\d x$ for some $V\in C^1(\R^d)$. Explicit sufficient conditions on $V$ and $\nu$ are presented such that $\mu*\nu$ satisfies the log-Sobolev, Poincar\'e…
We prove the reverse ultra log-concavity of the Boros-Moll polynomials. We further establish an inequality which implies the log-concavity of the sequence $\{i!d_i(m)\}$ for any $m\geq 2$, where $d_i(m)$ are the coefficients of the…
We show that there is a restriction, or modification of the finite-variable fragments of First Order Logic in which a weak form of Craig's Interpolation Theorem holds, but a strong form of this theorem does not hold. Translating these…
In this thesis new objects to the existing set of invariants of Lie algebras are added. These invariant characteristics are capable of describing the nilpotent parametric continuum of Lie algebras. The properties of these invariants, in…
We introduce the strength for sections of a line bundle on an algebraic variety. This generalizes the strength of homogeneous polynomials that has been recently introduced to resolve Stillman's conjecture, an important problem in…
We study the interplay between properties of measures on a Boolean algebra A and forcing names for ultrafilters on A. We show that several well known measure theoretic properties of Boolean algebras (such as supporting a strictly positive…
If a quantum system is prepared and later post-selected in certain states, "paradoxical" predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective…
We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.
We establish discrete and continuous log-concavity results for a biparametric extension of the $q$-numbers and of the $q$-binomial coefficients. By using classical results for the Jacobi theta function we are able to lift some of our…
This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of…
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…
In the field of categorical probability, one uses concepts and techniques from category theory, such as monads and monoidal categories, to study the structures of probability and statistics. In this paper, we connect some ideas from…
We introduce the class of {\em strongly Rayleigh} probability measures by means of geometric properties of their generating polynomials that amount to the stability of the latter. This class covers important models such as determinantal…