|
OALib Journal期刊
ISSN: 2333-9721
费用：99美元
|
|
|
|
实正交矩阵的子矩阵的幂的迹的渐进分布
, PP. 49-52
Keywords: 随机矩阵,实正交群,矩,正态分布,特征标
Abstract:
设随机矩阵U属于n阶实正交群O(n),O(n)的分布是单位Haar分布,［Um表示U的m阶顺序主子矩阵,记Q=nm［Um.文献(DiaconisP,ShahshahaniM.JApplProbab,1994,A3149-62.)通过计算TrUj的联合矩得出对固定的整数k,当n充分大时(TrU,TrU2,…,TrUk)渐进于正态分布.利用Jack函数和对称群的特征标的恒等式,推广这一结论到U的子矩阵情形,即证明了随机向量(TrQ,TrQ2,…,TrQk)当m→+∞时依分布收敛于正态分布.
| [1] | Hughes C P, Radnick Z. Mock Gaussian behaviour for linear statistics of classical compact groups[J]. J Phys,2003,A36:2919-2932.
|
| [2] | Pastur L, Vasilchuk V. On the moments of traces of matrices of classical Groups[J]. Commun Math Phys,2004,252:149-166.
|
| [3] | Stolz M. On the Diaconis-Shahshahani method in random matrix theory[J]. J Algebraic Combinatories,2005,22(4):471-191.
|
| [4] | Dehaye P O. Averages over classical compact Lie groups, twisted by characters[J]. J Combinatorial Theory,2007,A114(7):1278-1292.
|
| [5] | Feng Z M, Song J P. Integrals over the circular ensembles relating to classical domains[J]. J Phys,2009,A42:325204.
|
| [6] | Bai Z D, Silverstein J W. Spectral Analysis of Large Dimensional Random Matrices[M]. Beijing:Science Press,2006.
|
| [7] | Diaconis P, Evans S N. Linear functionals of eigenvalues of random matrices[J]. Trans Am Math Soc,2001,353:2615-2633.
|
| [8] | Diaconis P, Shahshahani M. On the eigenvalues of random matrices[J]. J Appl Probab,1994,A31:49-62.
|
| [9] | Diaconis P. Patterns in eigenvalues: The 70th Josiah Willard Gibbs lecture[J]. Bull Am Math Soc,2003,40(2):155-178.
|
| [10] | 冯志明. 典型群的迹的矩[J]. 乐山师范学院学报,2008,23(5):12-13.
|
| [11] | Collins B, Stolz M. Borel theorems for random matrices from the classical compact symmetric spaces[J]. Ann Probab,2008,36(3):876-895.
|
| [12] | Novak J. Truncations of random unitary matrices and Young tableaux[J]. Electronic J Combinatorics,2007,14:1-21.
|
| [13] | Jiang T F. How many entries of a typical orthogonal matrix can be approximated by independent normals[J]. Ann Probab,2006,34(4):1497-1529.
|
| [14] | Jiang T F. The entries of Haar-invariant matrices from the classical compact groups[J]. J Theo Probab,2010,23(4):1227-1243.
|
| [15] | Forrester P J. Quantum conductance problems and the Jacobi ensemble[J]. J Phys,2006,A39:6861-6870.
|
| [16] | Macdonald I G. Symmetric functions and Hall polynomials[M]. 2nd Ed. New York:Oxford University Press,1995.
|
Full-Text
|
|
Contact Us
service@oalib.com QQ:3279437679 
WhatsApp +8615387084133
|
|
