A CONTINUOUS SEMIGROUP OF NOTIONS OF INDEPENDENCE BETWEEN THE CLASSICAL AND THE FREE ONE

被引：14
|
作者：
Benaych-Georges, Florent [1 ,2 ]
Levy, Thierry [3 ,4 ]
机构：
[1] UPMC Univ Paris 6, LPMA, F-75252 Paris 05, France
[2] Ecole Polytech, F-91128 Palaiseau, France
[3] CNRS, F-75005 Paris, France
[4] Ecole Normale Super, DMA, F-75005 Paris, France
来源：
ANNALS OF PROBABILITY | 2011年 / 39卷 / 03期
关键词：
Free probability; independence; random matrices; unitary Brownian motion; convolution; cumulants; CALCULUS;
D O I：
10.1214/10-AOP573
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this paper, we investigate a continuous family of notions of independence which interpolates between the classical and free ones for noncommutative random variables. These notions are related to the liberation process introduced by Voiculescu. To each notion of independence correspond new convolutions of probability measures, for which we establish formulae and of which we compute simple examples. We prove that there exists no reasonable analogue of classical and free cumulants associated to these notions of independence.
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页码：904 / 938
页数：35
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