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A variance bound for a general function of independent noncommutative random variables (1811.00489v1)
Published 1 Nov 2018 in math.FA and math.OA
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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