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A variance bound for a general function of independent noncommutative random variables
- Source :
- Quaest. Math. 42 (2019), no. 3, 307--318
- Publication Year :
- 2018
-
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.<br />Comment: 15 pages (to appear in Quaest. Math.)
Details
- Database :
- arXiv
- Journal :
- Quaest. Math. 42 (2019), no. 3, 307--318
- Publication Type :
- Report
- Accession number :
- edsarx.1811.00489
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.2989/16073606.2018.1447044