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.

引用

页码：904 / 938

页数：35

共 50 条

[41] The study between ancient classical literature reading and perfect one's personality
Shen, Huizhen
[J]. PROCEEDINGS OF THE 2015 INTERNATIONAL CONFERENCE ON SOCIAL SCIENCE AND TECHNOLOGY EDUCATION (ICSSTE 2015), 2015, 18 : 81 - 84
[42] Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Continuous case
Godoy, E
Ronveaux, A
Zarzo, A
Area, I
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1997, 84 (02) : 257 - 275
[43] Practical assessment of evaluating free energy differences between classical and QM Hamiltonians
Cave-Ayland, Christopher
Skylaris, Chris-Kriton
Essex, Jonathan
[J]. ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY, 2015, 250
[44] DEGENERATION ON PASSING FROM A DISCRETE SPECTRUM TO A CONTINUOUS ONE AND TRANSITION FROM QUANTUM MECHANICS TO CLASSICAL MECHANICS
MASLOV, VP
[J]. DOKLADY AKADEMII NAUK SSSR, 1957, 114 (05): : 957 - 960
[45] THE THEORY OF CORRELATION BETWEEN 2 CONTINUOUS VARIABLES WHEN ONE IS DICHOTOMIZED
TATE, RF
[J]. BIOMETRIKA, 1955, 42 (1-2) : 205 - 216
[46] A note on the continuous extensions of injective morphisms between free groups to relatively free profinite groups
Coulbois, T
Sapir, M
Weil, P
[J]. PUBLICACIONS MATEMATIQUES, 2003, 47 (02) : 477 - 487
[47] EQUIVALENCE BETWEEN CONTINUOUS DISTRIBUTIONS OF DISLOCATIONS AND STRESS-FREE CRACKS
SMITH, E
[J]. INTERNATIONAL JOURNAL OF FRACTURE MECHANICS, 1972, 8 (01): : 107 - 109
[48] A NEW EXPONENTIAL SEPARATION BETWEEN QUANTUM AND CLASSICAL ONE-WAY COMMUNICATION COMPLEXITY
Montanaro, Ashley
[J]. QUANTUM INFORMATION & COMPUTATION, 2011, 11 (7-8) : 574 - 591
[49] ONE RELATIONSHIP BETWEEN INTENSITY COEFFICIENTS FOR PROBLEMS OF THE CLASSICAL AND MOMENT THEORY OF ELASTICITY.
Dudnikov, V.A.
Nazarov, S.A.
[J]. Mechanics of solids, 1983, 18 (03) : 187 - 189
[50] CONTINUOUS-REPRESENTATION THEORY .2. GENERALIZED RELATION BETWEEN QUANTUM AND CLASSICAL DYNAMICS
KLAUDER, JR
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1963, 4 (08) : 1058 - &

← 1 2 3 4 5 →