Φ-moment inequalities for independent and freely independent random variables

作者：Jiao, Yong^*; Sukochev, Fedor; Xie, Guangheng; Zanin, Dmitriy

来源：Journal of Functional Analysis, 2016, 270(12): 4558-4596.

DOI：10.1016/j.jfa.2016.02.001

• Phi-moment inequalities
• Johnson-Schechtman inequalities
• Free probability
• Kruglov operators

This paper is devoted to the study of Phi-moments of sums of independent/freely independent random variables. More precisely, let (f(k))(k=1)(n) be a sequence of positive (symmetrically distributed) independent random variables and let be an Orlicz function with Delta(2)-condition. We provide an equivalent expression for the quantity E(Phi(Sigma(n)(k=1) f(k))) in term of the sum of disjoint copies of the sequence (f(k))(k=1)(n). We also prove an analogous result in the setting of free probability. Furthermore, we provide an equivalent characterization of tau(Phi(sup(1 <= k <= n)(+) x(k))) for positive freely independent random variables and also present some new results on free Johnson Schechtman inequalities in the quasi-Banach symmetric operator space.

• 出版日期2016-6-15
• 单位中南大学