一个非交换鞅凸性不等式

IF 2.1 1区数学 Q1 STATISTICS & PROBABILITY

Annals of Probability Pub Date : 2014-05-02 DOI:10.1214/14-AOP990

'Eric Ricard, Quanhua Xu

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引用次数: 41

摘要

设M是一个具有忠实的半有限法向权φ的冯·诺伊曼代数，N是M的一个冯·诺伊曼子代数，使得φ对N的限制是半有限的，并且N对于φ的模群是不变的。作为一个应用，我们证明了存在e0>，使得对于任意自由群Fn且任意q≥4−e0，∥Pt∥2→q≤1⇔t≥logq−1−−−√，其中(Pt)是由Fn的自然长度函数定义的泊松半群。

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A noncommutative martingale convexity inequality

Let M be a von Neumann algebra equipped with a faithful semifinite normal weight ϕ and N be a von Neumann subalgebra of M such that the restriction of ϕ to N is semifinite and such that N is invariant by the modular group of ϕ. Let E be the weight preserving conditional expectation from M onto N. As an application we show that there exists e0>0 such that for any free group Fn and any q≥4−e0, ∥Pt∥2→q≤1⇔t≥logq−1−−−−√, where (Pt) is the Poisson semigroup defined by the natural length function of Fn.

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来源期刊

Annals of Probability 数学-统计学与概率论

CiteScore

4.60

自引率

8.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Annals of Probability publishes research papers in modern probability theory, its relations to other areas of mathematics, and its applications in the physical and biological sciences. Emphasis is on importance, interest, and originality – formal novelty and correctness are not sufficient for publication. The Annals will also publish authoritative review papers and surveys of areas in vigorous development.