Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection

被引：26

作者：

Belinschi, S. T. ^{[1
,2
]}

Popa, M. ^{[2
,3
]}

Vinnikov, V. ^{[4
]}

机构：

[1] Univ Saskatchewan, Dept Math & Stat, Saskatoon, SK S7N 5E6, Canada

[2] Romanian Acad, Inst Math Simion Stoilow, Bucharest 014700, Romania

[3] Ben Gurion Univ Negev, Ctr Adv Studies Math, IL-84105 Beer Sheva, Israel

[4] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Operator-valued free probability; Non-commutative functions; Limit theorems; Bercovici-Pata bijection; MONOTONIC INDEPENDENCE; LIMIT-THEOREMS; FREE-PRODUCTS; CONVOLUTION;

D O I：

10.1016/j.jfa.2011.09.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue for the Bercovici-Pata bijection. An important tool is Voiculescu's subordination property for operator-valued free convolution. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.

引用

页码：94 / 123

页数：30

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Akhieser N.I., 1965, CLASSICAL MOMENT PRO

[2]

[Anonymous], N HOLLAND MATH STUD

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