A variance bound for a general function of independent noncommutative random variables. Issue 3 (16th March 2019)

• Record Type: Journal Article
• Authors: Moslehian, Mohammad Sal; Talebi, Ali
• Is Part Of: Quaestiones mathematicae. Volume 42:Issue 3(2019)
• Page Start: 307
• Page End: 318
• Publication Date: 2019-03-16
• Subjects: Primary 46L53 -- Secondary 60E15; Efron-Stein inequality -- random matrix -- noncommutative probability -- trace -- conditional expectation; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2018.1447044
• Languages: English
• ISSNs: 1607-3606

Abstract

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.