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An algorithm for unification modulo one-sided distributivity is an early result by Tid\'en and Arnborg. More recently this theory has been of interest in cryptographic protocol analysis due to the fact that many cryptographic operators…
Effective bounds on the union probability are well known to be beneficial in the analysis of stochastic problems in many areas, including probability theory, information theory, statistical communications, computing and operations research.…
The literature on Dedekind sums is vast. In this expository paper we show that there is a common thread to many generalizations of Dedekind sums, namely through the study of lattice point enumeration of rational polytopes. In particular,…
Cumulants linearize convolution of measures. We use a formula of Good to define noncommutative cumulants in a very general setting.It turns out that the essential property needed is exchangeability of random variables. Roughly speaking the…
We consider a fractional counting process with jumps of amplitude $1,2,\ldots,k$, with $k\in \mathbb{N}$, whose probabilities satisfy a suitable system of fractional difference-differential equations. We obtain the moment generating…
We give an algorithm for properly learning Poisson binomial distributions. A Poisson binomial distribution (PBD) of order $n$ is the discrete probability distribution of the sum of $n$ mutually independent Bernoulli random variables. Given…
In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling. Our first result demonstrates that…
This paper presents foundational theoretical results on distributed parameter estimation for undirected probabilistic graphical models. It introduces a general condition on composite likelihood decompositions of these models which…
We study sums of independent random variables that take values $0$, $1/2$, or $1$. We show that the probability mass function of the sum splits into two interleaved parts: one supported on the integers and the other supported on the…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
We study a relaxation of the problem of coupling probability distributions -- a list of samples is generated from one distribution and an accept is declared if any one of these samples is identical to the sample generated from the other…
A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler's recurrence based on the pentagonal numbers, but where the…
We consider a component of the word statistics known as clump; starting from a finite set of words, clumps are maximal overlapping sets of these occurrences. This parameter has first been studied by Schbath with the aim of counting the…
This is a short survey on existing upper and lower bounds on the probability of the union of a finite number of events using partial information given in terms of the individual or pairwise event probabilities (or their sums). New proofs…
We show that the momentum sum rule is a necessary condition for factorization of double parton distributions into a product of two single parton distributions for small values of the parton momentum fractions x and large enough values of…
This paper presents an approach for the modelling of dependent random variables using generalised polynomial chaos. This allows to write chance-constrained optimization problems with respect to a joint distribution modelling dependencies…
The last success problem is an optimal stopping problem that aims to maximize the probability of stopping on the last success in a sequence of independent $n$ Bernoulli trials. In the classical setting where complete information about the…
A new version of a strong law of large numbers for a ``good'' pairwise independent sequence of random variables (r.v.'s) with a small part of ``bad'' dependent r.v.'s is proposed. The main goal is to relax the assumption on the existence of…
In this work, we revisit the problem of estimating the mean and covariance of an unknown $d$-dimensional Gaussian distribution in the presence of an $\varepsilon$-fraction of adversarial outliers. The pioneering work of [DKK+16] gave a…
Consider the homogeneous Boltzmann equation for Maxwellian molecules. We provide a new representation for its solution in the form of expectation of a random probability measure M. We also prove that the Fourier transform of M is a…