相关论文: Free Probability on a Direct Product of Noncommuta…
We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements $1,2,...,k$ are in distinct cycles of…
We consider eigenvalues of a product of n non-Hermitian, independent random matrices. Each matrix in this product is of size N\times N with independent standard complex Gaussian variables. The eigenvalues of such a product form a…
In this work we first give for PN spaces results parallel to those obtained by Egbert for the product of PM spaces, and generalize results by Alsina and Schweizer in order to study non-trivial products and the product of $m$-- transforms of…
The basic notions and results of equivariant KK-theory concerning crossed products can be extended to the case of locally compact quantum groups. We recall these constructions and prove some usefull properties of subgroups and amalgamated…
We study few properties of square-free integers in certain equations. Using this property, we derive some infinite products in powers of square free numbers. Also, we present a method, to convert power series and trigonometric series to…
Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…
Inspired by Lehner's results on exchangeability systems we define `weak conditional freeness' and `conditional freeness' for stationary processes in an operator algebraic framework of noncommutative probability. We show that these two…
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…
A valuation theoretic approach is presented that directly leads to division algebras that are noncrossed products (instead of, e.g., describing Brauer classes of noncrossed products in an abstract manner). While this feature is shared by…
Using the standard concepts of free random variables, we show that for a large class of nonhermitean random matrix models, the support of the eigenvalue distribution follows from their hermitean analogs using a conformal transformation. We…
We describe a simple approach to factorize non-commutative (nc) polynomials, that is, elements in free associative algebras (over a commutative field), into atoms (irreducible elements) based on (a special form of) their minimal linear…
We develop analytic tools for studying the free multiplicative convolution of any measure on the real line and any measure on the nonnegative real line. More precisely, we construct the subordination functions and the $S$-transform of an…
The main result of this paper is an explicit construction of the free commutative skew brace -- that is, a skew brace whose circle group is commutative -- on an arbitrary generating set $X$. We embed this object into a set of rational…
It is well known that for a given Poisson structure one has infinitely many star products related through the Kontsevich gauge transformations. These gauge transformations have an infinite functional dimension (i.e., correspond to an…
We calculate the microstates free entropy dimension of natural generators in an amalgamated free product of certain von Neumann algebras, with amalgamation over a hyperfinite subalgebra. In particular, some `exotic' Popa algebra generators…
The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a…
A reduction formula for compressions of von Neumann algebras arising as free products is proved. This shows that the fundamental group is all of the positive reals for some such algebras. Additionally, by taking a sort of free product with…
We give a method to obtain, from Voiculescu's inequality, norm estimates for sums of free variables with amalgamation in general fully symmetric spaces. We use these estimates to interpolate the Burkholder inequalities for non commutative…
The main aim of the article is to show, in the absence of the Axiom of Choice, relationships between the following, independent of $\mathbf{ZF}$, statements: "Every countable product of compact metrizable spaces is separable (respectively,…
We introduce two 2-variables transforms: the partial bi-free S-transform and the partial bi-free T-transform. These transforms are the analogues for the bi-multiplicative and respectively for the additive-multiplicative bi-free convolution…