Related papers: Construction of product $*$-probability spaces via…
This paper deals with (finite or infinite) sequences of arbitrary independent events in some probability space. We find sharp lower bounds for the probability of a union of such events when the sum of their probabilities is given. The…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
This paper introduces a space of variable lotteries and proves a constructive version of the expected utility theorem. The word ``constructive'' is used here in two senses. First, as in constructive mathematics, the logic underlying proofs…
This paper is devoted to the proof of the property of order separability for free product of free groups with maximal cyclic amalgamated subgroups.
Systems are typically made from simple components regardless of their complexity. While the function of each part is easily understood, higher order functions are emergent properties and are notoriously difficult to explain. In networked…
We describe a novel way to represent the probability distribution of a random binary string as a mixture having a maximally weighted component associated with independent (though not necessarily identically distributed) Bernoulli…
Growing dimensionality of data calls for beyond-pairwise interactions quantification. Measures of multidimensional interactions quantification are hindered, among others, by two issues: 1. Interpretation difficulties, 2. the curse of…
The cyclically reduced product of two words is the cyclically reduced form of the concatenation of the two words. While the reduced form of such a concatenation (which is the product of the free group) verifies many basic properties like…
It is obtained necessary and sufficient conditions of dependence on $\aleph$ coordinates for functions of several variables, each of which is a product of metrizable factors. The set of discontinuity points of such functions is…
In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality…
We show how to decompose any density matrix of the simplest binary composite systems, whether separable or not, in terms of only product vectors. We determine for all cases the minimal number of product vectors needed for such a…
An auxiliary free construction $*_{i=1}^{r}(K_i, L_i, t_i)_M$ based on HNN-extensions and on generalized free product of groups with amalgamated subgroups is suggested, and some of its basic properties are displayed. The proposed…
In this paper, we consider the following question and variants thereof: given $\mathbf D:=\big(a_{1;i}\otimes\cdots\otimes a_{K;i}:i\in I\big)$, a collection of elementary tensor non-commutative random variables in the tensor product of…
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…
We show that the deletion theorem of a free arrangement is combinatorial, i.e., whether we can delete a hyperplane from a free arrangement keeping freeness depends only on the intersection lattice. In fact, we give an explicit sufficient…
The main result of this paper is a generalization of Popa's free independence result for subalgebras of ultraproduct ${\rm II_1}$ factors [Po95] to the framework of ultraproduct von Neumann algebras $(M^\omega, \varphi^\omega)$ where $(M,…
Formal reasoning about hashing-based probabilistic data structures often requires reasoning about random variables where when one variable gets larger (such as the number of elements hashed into one bucket), the others tend to be smaller…
"Theorems for Free!" (Wadler, FPCA 1989) is a slogan for a technique that allows to derive statements about functions just from their types. So far, the statements considered have always had a purely extensional flavor: statements relating…
The partial copula provides a method for describing the dependence between two random variables $X$ and $Y$ conditional on a third random vector $Z$ in terms of nonparametric residuals $U_1$ and $U_2$. This paper develops a nonparametric…
Higher cumulants of conserved charges are sensitive observables of quantum chromodynamics phase transitions. The sample of mixed events provides a background to estimate non-critical effects of cumulants. Four possible methods for…