Related papers: Free Probability for Pairs of Faces I
Free probability provides a framework for describing correlations between non-commuting observables in complex quantum systems whose Hilbert-space states follow maximum-entropy distributions. We examine the robustness of this framework…
Likelihood-free inference refers to inference when a likelihood function cannot be explicitly evaluated, which is often the case for models based on simulators. Most of the literature is based on sample-based `Approximate Bayesian…
A notable result from analysis of Boolean functions is the Basic Invariance Principle (BIP), a quantitative nonlinear generalization of the Central Limit Theorem for multilinear polynomials. We present a generalization of the BIP for…
The present paper is mainly concerned with equations involving exponentials of bounded normal operators. Conditions implying commutativity of those normal operators are given. This is carried out without the known $2\pi i$-congruence-free…
A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows one to represent a density into independent and interactive parts, the former being built as the product of revised…
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…
We use the geometric concept of principal angles between subspaces to compute the noncommutative distribution of an expression involving two free projections. For example, this allows to simplify a formula by…
We show the existence of noncommutative random variables with finite free entropy but which do not generate a free group factor.
It is well known that while the independence of random variables implies zero correlation, the opposite is not true. Namely, uncorrelated random variables are not necessarily independent. In this note we show that the implication could be…
We argue that the concepts of "freedom of choice" and of "causal order" are intrinsically linked: a choice is considered "free" if it is correlated only to variables in its causal future. We discuss the implications of this to Bell-type…
This paper concerns free analytic maps on noncommutative domains. These maps are free analogs of classical holomorphic functions in several complex variables, and are defined in terms of noncommuting variables amongst which there are no…
We develop a theory of limits of finite posets in close analogy to the recent theory of graph limits. In particular, we study representations of the limits by functions of two variables on a probability space, and connections to…
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis…
Free choice (or statistical independence) assumption in a hidden variable model (HVM) means that the settings chosen by experimenters do not depend on the values of the hidden variable. The assumption of context-independent (CI) mapping in…
The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…
Let f be a cubic polynomial. Then there are infinitely many primes p such that f(p) is square-free.
We propose a new class of models for random permutations, which we call log-linear models, by the analogy with log-linear models used in the analysis of contingency tables. As a special case, we study the family of all Luce-decomposable…
Are there fundamentally random processes in nature? Theoretical predictions, confirmed experimentally, such as the violation of Bell inequalities, point to an affirmative answer. However, these results are based on the assumption that…
Simultaneous decompositions of a pair of states into pure ones are examined. There are privileged decompositions which are distinguished from all the other ones.
Likelihood-free methods perform parameter inference in stochastic simulator models where evaluating the likelihood is intractable but sampling synthetic data is possible. One class of methods for this likelihood-free problem uses a…