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1.
Necessary and sufficient conditions for convergence in distribution of products of i.i.d. d× d random circulant matrices are established here. The important role played by matrices in SO(d) is pointed out, and the validity of this result is shown to also hold for a class of Toeplitz matrices. 相似文献
2.
3.
Mark Skandera 《Journal of Algebraic Combinatorics》2004,20(2):195-211
Let
I,I be the minor of a matrix which corresponds to row set I and column set I. We give a characterization of the inequalities of the form
I,I
K,K
J,J
L,L
which hold for all totally nonnegative matrices. This generalizes a recent result of Fallat, Gekhtman, and Johnson. 相似文献
4.
Consider the ensemble of real symmetric Toeplitz matrices, each independent entry an i.i.d. random variable chosen from a
fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous investigations showed that the limiting spectral measure (the
density of normalized eigenvalues) converges weakly and almost surely, independent of p, to a distribution which is almost the standard Gaussian. The deviations from Gaussian behavior can be interpreted as arising
from obstructions to solutions of Diophantine equations. We show that these obstructions vanish if instead one considers real
symmetric palindromic Toeplitz matrices, matrices where the first row is a palindrome. A similar result was previously proved
for a related circulant ensemble through an analysis of the explicit formulas for eigenvalues. By Cauchy’s interlacing property
and the rank inequality, this ensemble has the same limiting spectral distribution as the palindromic Toeplitz matrices; a
consequence of combining the two approaches is a version of the almost sure Central Limit Theorem. Thus our analysis of these
Diophantine equations provides an alternate technique for proving limiting spectral measures for certain ensembles of circulant
matrices.
A. Massey’s current address: Department of Mathematics, UCLA, Los Angeles, CA 90095, USA. e-mail: amassey3102@math.ucla.edu. 相似文献
5.
利用随机的Bernstein多项式研究随机逼近问题具有一定的意义.借助弱收敛的概念,从分布函数的角度,讨论了随机Bernstein多项式依分布收敛问题.同时,与依概率收敛结果相比较,以此说明Bernstein多项式序列依分布收敛适用的范围更广. 相似文献
6.
假定F是一个由函数组成的集合.在这篇文章中,我们研究了指标集F上2阶的随机加权U-过程的条件弱收敛性质,导出了U-过程的随机加权逼近. 相似文献
7.
We study the asymptotic behaviour of points under matrix cocyles generated by rectangular matrices. In particular we prove a random Perron‐Frobenius and a Multiplicative Ergodic Theorem. We also provide an example where such products of random rectangular matrices arise in the theory of random walks in random environments and where the Multiplicative Ergodic Theorem can be used to investigate recurrence problems. 相似文献
8.
Let {vij}, i, j = 1, 2,…, be i.i.d. random variables with Ev11= 0, Ev112=1 and ai = (ai1,…,aiM) be random vectors with {aij} being i.i.d. random variables. Define XN=(x1,…, XK) and SN= XNXNT, where The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions. 相似文献
9.
For any probability on the space of d×d stochastic matrices we associate a probability
; on a finite group—a subgroup of the permutation group—related to the kernel of the semigroup generated by the support of . We show that n converges iff
n converges. 相似文献
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Consider the ensemble of real symmetric Toeplitz matrices whose entries are
i.i.d. random variable from a fixed probability distributionpof mean 0,variance 1, and finite moments of all order. The limiting spectral measure (the density of normalized eigenvalues) converges weakly to a new universal distribution with unbounded support, independent of pThis distribution’s moments are almost those of the Gaussian’s, and the deficit may be interpreted in terms of obstructions to Diophantine equations; the unbounded
support follows from a nice application of the Central Limit Theorem. With a little more work, we obtain almost sure convergence. An investigation of spacings between adjacent normalized eigenvalues looks Poissonian, and not GOE. A related ensemble (real symmetric palindromic Toeplitz matrices) appears to have no Diophantine obstructions, and the limiting spectral measure’s first nine moments can be shown to agree with those of the Gaussian; this will be considered in greater detail in a future paper. 相似文献
12.
Kelly Wieand 《Journal of Theoretical Probability》2003,16(3):599-623
We consider a class of random matrix ensembles which can be constructed from the random permutation matrices by replacing the nonzero entries of the n×n permutation matrix matrix with M×M diagonal matrices whose entries are random Kth roots of unity or random points on the unit circle. Let X be the number of eigenvalues lying in a specified arc I of the unit circle, and consider the standardized random variable (X–E[X])/(Var(X))1/2. We show that for a fixed set of arcs I
1,...,I
N
, the corresponding standardized random variables are jointly normal in the large n limit, and compare the covariance structures which arise with results for other random matrix ensembles. 相似文献
13.
B.Delyon J.Yao 《应用数学学报(英文版)》2006,22(2):297-312
We consider the empirical spectral distribution (ESD) of a random matrix from the Gaussian Unitary Ensemble. Based on the Plancherel-Rotaeh approximation formula for Hermite polynomials, we prove that the expected empirical spectral distribution converges at the rate of O(n^-1) to the Wigner distribution function uniformly on every compact intervals [u,v] within the limiting support (-1, 1). Furthermore, the variance of the ESD for such an interval is proved to be (πn)^-2 logn asymptotically which surprisingly enough, does not depend on the details (e.g. length or location) of the interval, This property allows us to determine completely the covariance function between the values of the ESD on two intervals. 相似文献
14.
对最大特征值的上下界进行估计是非负矩阵理论的重要部分,借助两个新的矩阵,从而得到一个判定非负矩阵最大特征值范围的界值定理,其结果比有关结论更加精确. 相似文献
15.
通过构造一个新的矩阵,从而得到一个非负矩阵最大特征值的估计法,该方法将适用范围推广到一般非负矩阵,并通过实例验证了这种新方法精确度更高. 相似文献
16.
Goldberg G. Okunev P. Neumann M. Schneider H. 《Methodology and Computing in Applied Probability》2000,2(2):137-151
We mainly investigate the behavior of the subdominant eigenvalue of matrices B= (b
i,j)n,n whose entries are independent random variables with an expectation Eb
i,j=1/n and with a variance n c/n
2 for some constant c 0. For such matrices we show that for large n, the subdominant eigenvalue is, with great probability, in a small neighborhood of 0. We also show that for large n, the spectral radius of such matrices is, with great probability, in a small neighborhood of 1. 相似文献
17.
文章针对特殊的非负矩阵,应月简单的相似变换,使矩阵保持非负性且最大行和减小,从而得到行和为正非负矩阵Perron根的新上界. 相似文献
18.
Let be a probability measure generating a locally compact semigroup S. If the convolution sequence
n
is tight, in particular if S is compact, S admits a closed minimal ideal K. The convergence of
n
is characterized in terms of convergence of a homomorphic image (~)
n
on a factor group of the compact group G in the Rees–Suschkewitsch decomposition of K. 相似文献
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20.
Some Geometry of the Cone of Nonnegative Definite Matrices and Weights of Associated X2 Distribution
Satoshi Kuriki Akimichi Takemura 《Annals of the Institute of Statistical Mathematics》2000,52(1):1-14
Consider the test problem about matrix normal mean M with the null hypothesis M = O against the alternative that M is nonnegative definite. In our previous paper (Kuriki (1993, Ann. Statist., 21, 1379–1384)), the null distribution of the likelihood ratio statistic has been given in the form of a finite mixture of 2 distributions referred to as X2 distribution. In this paper, we investigate differential-geometric structure such as second fundamental form and volume element of the boundary of the cone formed by real nonnegative definite matrices, and give a geometric derivation of this null distribution by virtue of the general theory on the X2 distribution for piecewise smooth convex cone alternatives developed by Takemura and Kuriki (1997, Ann. Statist., 25, 2368–2387). 相似文献