Related papers: Convolution comparison measures
We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels…
An analogue of the Berry-Esseen inequality is proved for the speed of convergence of free additive convolutions of bounded probability measures. The obtained rate of convergence is of the order n^{-1/2}, the same as in the classical case.…
In this paper we deal with free functional inequalities on the circle. There are some interesting changes as opposed to the classical case. For example, the free Poincar\'e inequality has a slight change which seems to account for the lack…
In this paper, we exhibit a new family of martingale couplings between two one-dimensional probability measures $\mu$ and $\nu$ in the convex order. This family is parametrised by two dimensional probability measures on the unit square with…
We investigate random Bernoulli convolutions, namely, probability measures given by the infinite convolution \[ \mu_\omega = \mathop{\circledast}_{k=1}^{\infty} \left( \frac{\delta_0 + \delta_{\lambda_1 \lambda_2 \ldots \lambda_{k-1}…
Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigorous theory of probability while the latter is not. In this…
A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when…
Classical confidence limits are compared to Bayesian error bounds by studying relevant examples. The performance of the two methods is investigated relative to the properties coherence, precision, bias, universality, simplicity. A proposal…
Let $X$ be a centered random variable with unit variance, zero third moment, and such that $E[X^4] \ge 3$. Let $\{F_n : n\geq 1\}$ denote a normalized sequence of homogeneous sums of fixed degree $d\geq 2$, built from independent copies of…
Deep insight can be gained into the nature of nonclassical correlations by studying the quantum operations that create them. Motivated by this we propose a measure of nonclassicality of a quantum operation utilizing the relative entropy to…
Let $s(n)$ denote the number of ones in the binary expansion of a natural number $n\in\mathbb{N}$. For any $t\in\mathbb{N}$ and $d\in\mathbb{Z}$, let $\mu_t(d)$ denote the asymptotic density of the set of those natural numbers $n$ for which…
This article extends the hypotheses assessment method to the case with two competing simple hypotheses. In doing so we further clarify the benefits that hypotheses assessments can bring to classical statistical analyses. Given that…
We solve two longstanding major problems in Free Probability. This is achieved by generalising the theory to one with values in arbitrary commutative algebras. We prove the existence of the multi-variable $S$-transform, and show that it is…
In this note we present an algorithm to obtain a uniform lower bound on Hausdorff dimension of the stationary measure of an affine iterated function scheme with similarities, the best known example of which is Bernoulli convolution. The…
In classical mechanics, performing a measurement without reading the measurement outcome is equivalent to not exploiting the measurement at all. A non-selective measurement in the classical realm carries no information. Here we show that…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…
We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by semi-norms which are defined by a combination of classical norms and multiplication or…
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means $\{ \mu_1, \mu_2, \mu_3\}$ through an analysis of variance…