相关论文: Extreme Points of the Convex Set of Joint Probabil…

We show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy. These maximum and minimum values are obtained for two standard forms of probability distribution (or…

Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…

In this paper we characterize the extremal points of the unit ball of the Benamou--Brenier energy and of a coercive generalization of it, both subjected to the homogeneous continuity equation constraint. We prove that extremal points…

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are…

We consider a generalization of the Bauer maximum principle. We work with tensorial products of convex measures sets, that are non necessarily compact but generated by their extreme points. We show that the maximum of a quasi-convex lower…

We prove two related concentration inequalities concerning the number of rational points of hyperelliptic curves over subsets of a finite field. In particular, we investigate the probability of a large discrepancy between the numbers of…

In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…

This paper deals with (finite or infinite) sequences of arbitrary independent events in some probability space. We find sharp lower bounds for the probability of a union of such events when the sum of their probabilities is given. The…

We will consider completely positive maps defined on tensor products of von Neumann algebras and taking values in the algebra of bounded operators on a Hilbert space and particularly certain convex subsets of the set of such maps. We show…

The thesis concentrates on two problems in discrete geometry, whose solutions are obtained by analytic, probabilistic and combinatoric tools. The first chapter deals with the strong polarization problem. This states that for any sequence…

The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…

We study the convex polytope of n x n stochastic matrices that define locally differentially private mechanisms. We first present invariance properties of the polytope and results reducing the number of constraints needed to define it. Our…

For a pair of coupled rectangular random matrices we consider the squared singular values of their product, which form a determinantal point process. We show that the limiting mean distribution of these squared singular values is described…

Generalized entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…

We consider all totally asymmetric simple exclusion processes (TASEPs) whose transition probabilities are given in the Sch\"utz-type formulas and which jump with homogeneous rates. We show that the multi-point distribution of particle…

We study the universal closest refinement problem on measurable bipartite relations over standard Borel spaces. Given prescribed side measures, the feasible class consists of finite refinement plans concentrated on the relation and carrying…

A partial differential equation governing the global evolution of the joint probability distribution of an arbitrary number of local flow observations, drawn randomly from a control volume, is derived and applied to examples involving…

This paper establishes novel fixed point theorems for Kannan-type and Chatterjea-type mappings in probabilistic cone metric spaces. By integrating probabilistic distance functions with cone-valued structures, we generalize classical fixed…