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


Mohammad Sal Moslehian
Ali Talebi

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.

Mathematics Subject Classification (2010): Primary 46L53; Secondary 60E15.

Keywords: Efron-Stein inequality, random matrix, noncommutative probability, trace, conditional expectation


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eISSN: 1727-933X
print ISSN: 1607-3606