Results 1 to 10 of about 24 (23)

A variance bound for a general function of independent noncommutative random variables

Quaestiones Mathematicae, 2019
The main purpose of this paper is to establish a noncommutative analogue of the Efron-Stein inequality, which bounds the variance of a general function of some independent random variables. Moreover, we state an operator version including random matrices,
Mohammad Sal Moslehian, Ali Talebi
exaly   +1 more source

An equivalent quasinorm for the Lipschitz space of noncommutative martingales

Open Mathematics, 2020
In this paper, an equivalent quasinorm for the Lipschitz space of noncommutative martingales is presented. As an application, we obtain the duality theorem between the noncommutative martingale Hardy space hpc(ℳ){h}_{p}^{c}( {\mathcal M} ) (resp.
Ma Congbian, Ren Yanbo
doaj   +1 more source

Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs

Special Matrices, 2015
In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the
Cho Ilwoo, Jorgensen Palle E. T.
doaj   +1 more source

Matrices induced by arithmetic functions acting on certain Krein spaces

Special Matrices, 2017
In this paper, we study matrices induced by arithmetic functions under certain Krein-space representations induced by (multi-)primes less than or equal to fixed positive real numbers.
Cho Ilwoo
doaj   +1 more source

Krein-space operators determined by free product algebras induced by primes and graphs

Special Matrices, 2017
In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number ...
Cho Ilwoo, Jorgensen Palle E. T.
doaj   +1 more source

The ergodic theorem for random walks on finite quantum groups

Communications in Algebra, 2021
J P Mccarthy
exaly  

On superconvergence of sums of free random variables

Annals of Probability, 2007
Vladislav Kargin
exaly  

Rosenthal's theorem for subspaces of noncommutative Lp

Duke Mathematical Journal, 2008
Marius Junge, Javier Parcet
exaly  

Askey–Wilson polynomials, quadratic harnesses and martingales

Annals of Probability, 2010
Włodzimierz Bryc, Jacek WESOŁOWSKI
exaly  

Noncommutative Burkholder/Rosenthal inequalities

Annals of Probability, 2003
Marius Junge, Quanhua Xu
exaly