Article

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

Published in: Quaestiones Mathematicae
Volume 42 , issue 3 , 2019 , pages: 307–318

DOI: 10.2989/16073606.2018.1447044

Author(s): Mohammad Sal Moslehian Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Iran , Ali Talebi Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Iran

Keywords: Primary 46L53 , Secondary 60E15 , Primary 46L53 , Secondary 60E15

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Abstract

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, which extends a result of D. Paulin et al., [Ann. Probab. 44(5) (2016), 3431–3473]. Further, we state a Steele type inequality in the framework of noncommutative probability spaces.

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