Related papers: On Boolean selfdecomposable distributions
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 develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…
We characterize the symmetric distributions that can be (approximately) generated by shallow Boolean circuits. More precisely, let $f\colon \{0,1\}^m \to \{0,1\}^n$ be a Boolean function where each output bit depends on at most $d$ input…
In this thesis we study convolutions that arise from noncommutative probability theory. We prove several regularity results for free convolutions, and for measures in partially defined one-parameter free convolution semigroups. We discuss…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…
In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…
In the probability theory \emph{selfdecomposable, or class $L_0$ distributions} play an important role as they are limiting distributions of normalized partial sums of sequences of independent, not necessarily identically distributed,…
A probability distribution $\mu$ on $\mathbb R ^d$ is selfdecomposable if its characteristic function $\widehat\mu(z), z\in\mathbb R ^d$, satisfies that for any $b>1$, there exists an infinitely divisible distribution $\rho_b$ satisfying…
The notion of random self-decomposability is generalized here. Its relation to self-decomposability, Harris infinite divisibility and its connection with a stationary first order generalized autoregressive model are presented. The notion is…
The well known Boole-Shannon expansion of Boolean functions in several variables (with co-efficients in a Boolean algebra $B$) is also known in more general form in terms of expansion in a set $\Phi$ of orthonormal functions. However,…
We investigate variance bounds under symmetry constraints in classical, free, and Boolean probability, focusing on Bernoulli distributions and their noncommutative analogues, projections with trace \(p\). We show that symmetrizers under…
Probability distributions supported on the simplex enjoy a wide range of applications across statistics and machine learning. Recently, a novel family of such distributions has been discovered: the continuous categorical. This family enjoys…
In this paper, we investigate in a unified way the structural properties of solutions to inverse problems. These solutions are regularized by the generic class of semi-norms defined as a decomposable norm composed with a linear operator,…
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…
We prove that the convolution of a selfdecomposable distribution with its background driving law is again selfdecomposable if and only if the background driving law is s-selfdecomposable. We will refer to this as the \textit{factorization…
The Bernoulli convolution with parameter $\lambda\in(0,1)$ is the measure on $\bf R$ that is the distribution of the random power series $\sum\pm\lambda^n$, where $\pm$ are independent fair coin-tosses. This paper surveys recent progress on…
When approximating the joint distribution of the component counts of a decomposable combinatorial structure that is `almost' in the logarithmic class, but nonetheless has irregular structure, it is useful to be able first to establish that…
We show that Boolean functions expressible as monotone disjunctive normal forms are PAC-evolvable under a uniform distribution on the Boolean cube if the hypothesis size is allowed to remain fixed. We further show that this result is…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…