Related papers: Graph Free Product of Noncommutative Probability s…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…
A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general representation of the collection of non-negative weighted…
In this paper, we study the structure of the complete asymptotic expansion of the probability that a large combinatorial object is connected or consists of a given number of connected components. For rapidly growing labeled families of…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
In this work we extend the recently introduced group-theoretical approach to moment-cumulant relations in non-commutative probability theory to the notion of conditionally free cumulants. This approach is based on a particular combinatorial…
First, we review the notion of a Poisson structure on a noncommutative algebra due to Block-Getzler and Xu and introduce a notion of a Hamiltonian vector field on a noncommutative Poisson algebra. Then we describe a Poisson structure on a…
Degree-based graph construction is an ubiquitous problem in network modeling, ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive…
We apply the free product construction to various local algebras in algebraic quantum field theory. If we take the free product of infinitely many identical half-sided modular inclusions with ergodic canonical endomorphism, we obtain a…
Compositional graphoids are fundamental discrete structures which appear in probabilistic reasoning, particularly in the area of graphical models. They are semigraphoids which satisfy the Intersection and Composition properties. These…
A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be…
We introduce the concept of a pants decomposition for a finitely generated free group and construct the corresponding pants graph. A pants decomposition of a free group leads to the formation of a simplicial graph, referred to as the pants…
In this paper, we pursue our study of asymptotic properties of families of random matrices that have a tensor structure. In previous work, the first- and second-named authors provided conditions under which tensor products of unitary random…
In this paper, we define a Hopf algebra structure on the vector space spanned by packed words using a selection-quotient coproduct. We show that this algebra is free on its irreducible packed words. Finally, we give some brief explanations…
A general random graph evolution mechanism is defined. The evolution is a combination of the preferential attachment model and the interaction of N vertices (N>=3). A vertex in the graph is characterized by its degree and its weight. The…
It is assumed that under suitable economic and information-theoretic conditions, market exchange rates are free from arbitrage. Commodity markets in which trades occur over a complete graph are shown to be trivial. We therefore examine the…
We introduce a combinatorial criterion for verifying whether a formula is not the conjunction of an equation and a co-equation. Using this, we give a proof for the nonequationality of the free group. Furthermore, we generalize the latter…
We establish a combinatorial model for the Boardman--Vogt tensor product of several absolutely free operads, that is free symmetric operads that are also free as $\mathbb{S}$-modules. Our results imply that such a tensor product is always a…
We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from…
An "element-free" probability distribution is what remains of a probability distribution after we forget the elements to which the probabilities were assigned. These objects naturally arise in Bayesian statistics, in situations where…
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…