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arXiv · 1811.00489

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

Ali Talebi·Mohammad Sal Moslehian
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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 (2016), no. 5, 3431--3473]. Further, we state a Steele type inequality in the framework of noncommutative probability spaces.

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Ali Talebi, Mohammad Sal Moslehian. 2018-11-01. A variance bound for a general function of independent noncommutative random variables. https://doi.org/10.2989/16073606.2018.1447044

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