相关论文: How Free-Free-Boolean Independence Arises in Bi-Fr…
Possibilistic conditional independence is investigated: we propose a definition of this notion similar to the one used in probability theory. The links between independence and non-interactivity are investigated, and properties of these…
Ideals in the ring of power series in three variables can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense that it remains open which algebra structures actually…
We describe, up to degree equal to the rank, the Lie algebra associated with the automorphism group of a free group. We compute in particular the ranks of its homogeneous components, and their structure as modules over the linear group.…
Wick polynomials and Wick products are studied in the context of non-commutative probability theory. It is shown that free, boolean and conditionally free Wick polynomials can be defined and related through the action of the group of…
We prove a free analogue of Brillinger's formula (sometimes called "law of total cumulance") which expresses classical cumulants in terms of conditioned cumulants. As expected, the formula is obtained by replacing the lattice of set…
We classify (up to quasi-isomorphism) the free differential modules whose homology is equal to a given module $M$ by developing a theory for deforming an arbitrary free complex into a differential module. We use an iterative approach to…
Starting from elementary considerations about independence and Markov processes in classical probability we arrive at the new concept of conditional monotone independence (or operator-valued monotone independence). With the help of product…
We consider the zeros of the sum of independent random polynomials as their degrees tend to infinity. Namely, let $p$ and $q$ be two independent random polynomials of degree $n$, whose roots are chosen independently from the probability…
We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different…
In this article, we establish a Liouville-type inequality for polynomials evaluated at the values of arbitrary Siegel E-functions at non-zero algebraic points. Additionally, we provide a comparable result within the framework of Mahler M…
We study the structure of the inverse limit of the graded algebras of local unitary invariant polynomials using its Hilbert series. For k subsystems, we conjecture that the inverse limit is a free algebra and the number of algebraically…
In an independence model, the triplets that represent conditional independences between singletons are called elementary. It is known that the elementary triplets represent the independence model unambiguously under some conditions. In this…
This paper introduces the notion of pseudo-independence on the sublinear expectation space $(\Omega,\mathcal{F},\mathcal{P})$ via the classical conditional expectation, and the relations between pseudo-independence and Peng's independence…
In this paper we give an analytic interpretation of free convolution of type B, introduced by Biane, Goodman and Nica, and provide a new formula for its computation. This formula allows us to show that free additive convolution of type B is…
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…
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…
The aim of this article is to introduce Hall bases of free Leibniz algebras. We modify the classical notion of Hall bases for free Lie algebras in order to provide the similar construction for the case of Leibniz algebras.
The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-differential algebra with a weight, in analogy to the…
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 article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…