可微非交换概率空间中的半单位圆和单位圆元素
Semicircular and Circular Elements in Infinitesimal Non-commutative Probability Space
摘要
在可微非交换概率空间(INCPS)中,证明了彼此自由独立的标准半单位圆元素的和与乘积仍然是半单位圆元素。在INCPS中定义了单位圆元素,并给出了它在矩函数形式下的交错乘积的*-分布。
In an infinitesimal non-commutative probability space, the sum and product of semicircular elements which are infinitesimally free is still a semicircular element. The circular elements in an infinitesimal non-commutative probability space are also defined. Distribution of its alternating products is given in the form of moments.
出处
《上海电机学院学报》
2010年第3期170-173,共4页
Journal of Shanghai Dianji University
关键词
可微非交换概率空间
半单位圆元素
单位圆元素
累计函数
矩函数
infinitesimal non-commutative probability space
semicircular elements
circular element
eumulants
moments
参考文献8
-
1Hiai F, Petz D. The semicircle law, free random variables and entropy[M]. Providence RI: American Mathematical Society, 2000.
-
2Speicher R. Multiplicative functions on the lattice of non-crossing partitions and free convolution[J]. Mathematische Annalen, 1994,298 (1) : 611-628.
-
3Nica A, Speicher R. Lectures on the combinatorics of free probability: London Mathematical Society Lecture Note Series[M]. Cambridge:Cambridge University Press, 2006.
-
4Reiner V. Non-crossing partitions for classical reflection groups[J]. Discrete Mathematics, 1997, 177(1/3) : 195-222.
-
5Biane P, Goodman F, Nica A. Non-crossing cumulants of type B[J]. Transactions of the American Mathematical Society, 2003,355(6): 2263-2303.
-
6Belinschi ST, Shlyakhtenko D. Free probability of type B: analytic aspects and applications[EB/OL].(2009-03-16) [2010-04-02]. http://arXiv.org/ pdf/0903. 2721.
-
7Fevrier M, Nica A. Infinitesimal non-crossing cumulants and free probability of Type B[EB/OL]. (2009-06-10)[2010-04-02]. http://arXiv. org/ pdf/0906. 2017.
-
8Stanley R P. Enumerative combinatorics, Cambridge studies in advanced mathematics[M]. Cambridge: Cambridge University Press, 1997.
