Related papers: Lower cone distribution functions and set-valued q…
Classes of multivariate and cone valued infinitely divisible Gamma distributions are introduced. Particular emphasis is put on the cone-valued case, due to the relevance of infinitely divisible distributions on the positive semi-definite…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
The most striking feature of quark distribution functions transformed to the longitudinal distance representation is the recognizable separation of small and large longitudinal distances. While the former are responsible for the average…
The distribution of individual Dirac eigenvalues is derived by relating them to the density and higher eigenvalue correlation functions. The relations are general and hold for any gauge theory coupled to fermions under certain conditions…
This paper establishes quantitative correlation inequalities between monotone events and structured threshold objects in both the discrete cube and Gaussian space. We prove that for any increasing balanced family, there exists a linear…
We introduce a nonasymptotic framework for sub-Poisson distributions with moment generating function dominated by that of a Poisson distribution. At its core is a new notion of optimal sub-Poisson variance proxy, analogous to the variance…
We prove an exact relationship between the optimal denoising function and the data distribution in the case of additive Gaussian noise, showing that denoising implicitly models the structure of data allowing it to be exploited in the…
Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth.This fact motivates the consideration of subdifferentials for such typically just continuous…
Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…
A Galois connection between clones and relational clones on a fixed finite domain is one of the cornerstones of the so-called algebraic approach to the computational complexity of non-uniform Constraint Satisfaction Problems (CSPs). Cohen…
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…
Karlin and Altschul in their statistical analysis for multiple high-scoring segments in molecular sequences introduced a distribution function which gives the probability there are at least r distinct and consistently ordered segment pairs…
We use an idea from sieve theory to estimate the distribution of the lengths of $k$th shortest vectors in a random lattice of covolume 1 in dimension $n$. This is an improvement of the results of Rogers and S\"odergren in that it allows $k$…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
This paper presents a connection between Galois points and rational functions over a finite field with small value sets. This paper proves that the defining polynomial of any plane curve admitting two Galois points is an irreducible…
It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…
In this paper we derive tight bounds on the expected value of products of {\em low influence} functions defined on correlated probability spaces. The proofs are based on extending Fourier theory to an arbitrary number of correlated…
We show that if the zeros of an automorphic $L$-function are weighted by the central value of the $L$-function or a quadratic imaginary base change, then for certain families of holomorphic GL(2) newforms, it has the effect of changing the…
We show a general phenomenon of the constrained functional value for densities satisfying general convexity conditions, which generalizes the observation in Bobkov and Madiman (2011) that the entropy per coordinate in a log-concave random…