Related papers: Operator-valued free multiplicative convolution: a…
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…
We extend the free difference quotient coalgebra approach to analytic subordination to the case of a free compression in free probability.
We study the freely infinitely divisible distributions that appear as the laws of free subordinators. This is the free analog of classically infinitely divisible distributions supported on [0,\infty), called the free regular measures. We…
We study of the connection between operator valued central limits for monotone, Boolean and free probability theory, which we shall call the arcsine, Bernoulli and semicircle distributions, respectively. In scalar-valued non-commutative…
We define an extension of the polynomial calculus on a W*-probability space by introducing an abstract algebra which contains polynomials. This extension allows us to define transition operators for additive and multiplicative free…
We study matricial approximations of master fields we constructed in a previous work. These approximations (in non-commutative distribution) are obtained by extracting blocks of a Brownian unitary diffusion (with entries in $\mathbb{R},…
Different types of convolution operations involving large Vandermonde matrices are considered. The convolutions parallel those of large Gaussian matrices and additive and multiplicative free convolution. First additive and multiplicative…
Motivated by a random matrix theory model from wireless communications, we define random operator-valued matrices as the elements of $L^{\infty-}(\Omega,{\mathcal F},{\mathbb P}) \otimes M_d({\mathcal A})$ where $(\Omega,{\mathcal…
An operadic framework is developed to explain the inversion formula relating moments and cumulants in operator-valued free probability theory.
We consider the infinitesimal freeness in the operator-valued framework, and we show that the operator-valued infinitesimal (OVI) free independence is equivalent to the operator-valued free independence over an algebra of $2\times 2$ upper…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
In this paper we present a novel derivation for an existing node-based algorithm for distributed optimisation termed the primal-dual method of multipliers (PDMM). In contrast to its initial derivation, in this work monotone operator theory…
Based on the~method of subordinating functions we prove bounds for the minimal error of approximations of $n$-fold convolutions of probability measures by free infinitely divisible probability measures.
Finite-free additive and multiplicative convolutions are operations on the set of polynomials with real roots, introduced independently by Szeg\"{o} and Walsh in the 1920s. These operations have regained some interest, in the last decade,…
In this paper, a connection between bi-free probability and the theory of non-commutative stochastic processes is examined. Specifically it is demonstrated that the transition operators for non-commutative stochastic processes can be…
A duality transform for the coalgebra of the free difference quotient derivation-multiplication of an operator with respect to a free algebra of scalars is constructed. The dual object is realized in an algebra of matricial analytic…
In this paper, we introduce the new construction of fractional derivatives and integrals with respect to a function, based on a matrix approach. We believe that this is a powerful tool in both analytical and numerical calculations. We begin…
We propose periodic Macdonald processes as a $(q,t)$-deformation of periodic Schur processes and a periodic analogue of Macdonald processes. It is known that, in the theory of stochastic processes related to a family of symmetric functions,…
We extend an algebra of Mantaci and Reutenauer, acting on the free associative algebra, to a vector space of operators acting on all graded connected Hopf algebras. These operators are convolution products of certain involutions, which we…
Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no…