English

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

Functional Analysis 2021-07-23 v1 Operator Algebras

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.

Keywords

Cite

@article{arxiv.1811.00489,
  title  = {A variance bound for a general function of independent noncommutative random variables},
  author = {Ali Talebi and Mohammad Sal Moslehian},
  journal= {arXiv preprint arXiv:1811.00489},
  year   = {2021}
}

Comments

15 pages (to appear in Quaest. Math.)

R2 v1 2026-06-23T05:00:58.805Z