Characterization of non-commutative free Gaussian variables

被引：0
|
作者：
Bose, Arup [1 ]
Dey, Apratim [1 ]
Ejsmont, Wiktor [2 ]
机构：
[1] Indian Stat Inst, 203 BT Rd, Kolkata 700108, India
[2] Univ Wroclaw, Math Inst, Pl Grunwaldzki 2-4, PL-50384 Wroclaw, Poland
来源：
ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS | 2018年 / 15卷 / 02期
关键词：
Basu's theorem; free independence; free Gaussian; free cumulants; Mobius function; polynomial identity; operator-valued non-commutative probability space; FREE PROBABILITY; LAWS;
D O I：
10.30757/ALEA.v15-46
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：
We provide a necessary and sufficient condition, based on zero correlation, for self-adjoint, freely independent, identically distributed random variables on a *-probability space to be free Gaussian. Along the way, we establish a free analogue of a well known application of Basu's theorem from statistics. We also show that all linear combinations of free Gaussian being free Gaussian does not necessarily imply joint free Gaussianity, and we identify additional conditions under which this implication is true.
引用
收藏
页码：1241 / 1255
页数：15
相关论文
共 50 条
  • [1] Universality of free random variables: Atoms for non-commutative rational functions
    Arizmendi, Octavio
    Cebron, Guillaume
    Speicher, Roland
    Yin, Sheng
    [J]. ADVANCES IN MATHEMATICS, 2024, 443
  • [2] Non-commutative functions and the non-commutative free Levy-Hincin formula
    Popa, Mihai
    Vinnikov, Victor
    [J]. ADVANCES IN MATHEMATICS, 2013, 236 : 131 - 157
  • [3] Symbolic computing with anti-commutative and non-commutative variables
    Cheb-Terrab, ES
    [J]. MAPLETECH, 1998, 5 (01): : 16 - 22
  • [4] A NON-COMMUTATIVE ANALOGUE OF GAUSSIAN HILBERT SPACES
    Popa, Mihai
    [J]. OPERATOR THEORY 20, PROCEEDINGS, 2006, : 171 - 180
  • [5] Simplification of symbolic polynomials on non-commutative variables
    de Oliveira, Mauricio C.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 437 (07) : 1734 - 1748
  • [6] Dual Lukacs regressions for non-commutative variables
    Szpojankowski, Kamil
    Wesolowski, Jacek
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (01) : 36 - 54
  • [7] Bekenstein Bound and Non-Commutative Canonical Variables
    Scardigli, Fabio
    [J]. UNIVERSE, 2022, 8 (12)
  • [8] Unconstrained variables of non-commutative open strings
    De Andrade, MA
    Santos, MA
    Vancea, IV
    [J]. JOURNAL OF HIGH ENERGY PHYSICS, 2001, (06):
  • [9] EXTENSION OF CLASSICAL POLYNOMIALS TO NON-COMMUTATIVE VARIABLES
    LENORMAND, C
    [J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1977, 285 (04): : 161 - 164
  • [10] Limit Theorems for Non-Commutative Random Variables
    A. Coja-Oghlan
    J. Michaliček
    [J]. Journal of Theoretical Probability, 2005, 18 : 595 - 614
12345