共查询到20条相似文献,搜索用时 15 毫秒
1.
对于判断矩阵重特征值的存在性问题,运用“若λ是矩阵A的特征值,则入“是Ak的特征值”这一性质,通过矩阵的迹与特征值的关系,得到了实数域上矩阵重特征值的存在性定理并给出了证明.定理实现了“由矩阵幂运算来判断矩阵重特征值的存在性”这样一个计算过程,对讨论矩阵特征值问题具有一定的启示意义. 相似文献
2.
A. Astrauskas 《Lithuanian Mathematical Journal》1999,39(2):117-133
Let
, be the mean-field Hamiltonian with
and random i.i.d. potential ξV. We prove limit theorems for the extreme eigenvalues of
as |V|→∞. The limiting distributions are the same as for the corresponding extremes of ξV only if either (i) ξV is undbounded and
, or (ii) ξV is bounded with “sharp” peaks and
. Localization properties for the corresponding eigenfunctions are also studied.
Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys,
Vol. 39, No. 2, pp. 147–168, April–June, 1999. 相似文献
3.
XIE JunShan 《中国科学 数学(英文版)》2014,57(6):1221-1236
This paper focuses on the dilute real symmetric Wigner matrix Mn=1√n(aij)n×n,whose offdiagonal entries aij(1 i=j n)have mean zero and unit variance,Ea4ij=θnα(θ0)and the fifth moments of aij satisfy a Lindeberg type condition.When the dilute parameter 0α13and the test function satisfies some regular conditions,it proves that the centered linear eigenvalue statistics of Mn obey the central limit theorem. 相似文献
4.
Michael Drmota Bernhard Gittenberger Thomas Klausner. 《Mathematics of Computation》2005,74(252):1953-1966
We consider an extension of Hayman's notion of admissibility to bivariate generating functions that have the property that the coefficients satisfy a central limit theorem. It is shown that these admissible functions have certain closure properties. Thus, there is a large class of functions for which it is possible to check this kind of admissibility automatically. This is realized with help of a MAPLE program that is also presented. We apply this concept to various combinatorial examples.
5.
高斯过程函数的中心极限定理与应用 总被引:1,自引:0,他引:1
采用Wiener空间的两个算子以及相关的恒等式,提出了新的方法证明了关于高斯过程函数的中心极限定理,并给出了该中心极限定理的应用实例. 相似文献
6.
Armando Machado 《Linear and Multilinear Algebra》2013,61(6):561-566
We present an elementary proof of the existence of an eigenvalue for an endomorphism of a complex vector space and we derive the Fundamental Theorem of Algebra as a corollary of this existence. We also present new proofs for the corresponding results for endomorphisms of real vector spaces. 相似文献
7.
Steven J. Sepanski 《Journal of Theoretical Probability》1999,12(3):757-778
For a sequence of independent identically distributed random vectors, we prove that the limiting cluster set of the appropriately operator normed partial sums is, with probability one, the closed unit euclidean ball. The result is proved under the hypotheses that the law of the random vectors belongs to the Generalized Domain of Attraction of the multivariate Gaussian law and satisfy a mild integrability condition. The two conditions together are still weaker than finite second normed moment and are necessary and sufficient. 相似文献
8.
Rita Giuliano Claudio Macci Barbara Pacchiarotti 《Journal of Mathematical Analysis and Applications》2014
In this paper we study some sequences of weighted means of continuous real valued Gaussian processes. More precisely we consider suitable generalizations of both arithmetic and logarithmic means of a Gaussian process with covariance function which satisfies either an exponential decay condition or a power decay condition. Our aim is to provide limits of variances of functionals of such weighted means which allow the application of some large deviation results in the literature. 相似文献
9.
《Journal of Computational and Applied Mathematics》1994,50(1-3):51-66
The paper deals with the finite-element analysis of second-order elliptic eigenvalue problems when the approximate domains Ωh are not subdomains of the original domain
. The considerations are restricted to piecewise linear approximations. Special attention is devoted to the convergence of approximate eigenfunctions in the case of multiple exact eigenvalues. As yet the approximate solutions have been compared with linear combinations of exact eigenfunctions with coefficients depending on the mesh parameter h. We avoid this disadvantage. 相似文献
10.
11.
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.
This paper presents limit theorems for realized power variation of processes of the form Xt=t0φsdGs+ξt as the sampling frequency within a fixed interval increases to infinity.Here G is a Gaussian process with stationary increments,ξis a purely non-Gaussian L′evy process independent from G,andφis a stochastic process ensuring that the integral is well defined as a pathwise Riemann-Stieltjes integral.We obtain the central limit theorems for the case that both the continuous term and the jump term are presented simultaneously in the law of large numbers. 相似文献
13.
E.K. Ifantis C.G. Kokologiannaki E. Petropoulou 《Central European Journal of Mathematics》2007,5(2):335-344
Let T be a self-adjoint tridiagonal operator in a Hilbert space H with the orthonormal basis {e
n
}
n=1
∞
, σ(T) be the spectrum of T and Λ(T) be the set of all the limit points of eigenvalues of the truncated operator T
N
. We give sufficient conditions such that the spectrum of T is discrete and σ(T) = Λ(T) and we connect this problem with an old problem in analysis.
相似文献
14.
W. Dunsmuir 《Stochastic Processes and their Applications》1983,14(3):279-295
The central limit theorem is proved for estimates of parameters which specify the covariance structure of a zero mean, stationary, Gaussian, discrete time series observed at unequally spaced times. The estimates considered are obtained by a single iteration from consistent estimates. The result also applies to the maximum likelihood estimate if it is consistent although consistency is not proved here. The essential condition on the sampling times is that the finite sample information matrix, when divided by the sample size, has a limit which is nonsingular and has finite norm. Some examples are presented to illustrate this condition. 相似文献
15.
16.
A. Mačiulis 《Lithuanian Mathematical Journal》1999,39(1):58-63
The convergence of the value distributions of a normalized sequence of strongly additive arithmetic functions to the standard normal law in theL p metric is considered. An asymptotic formula for the variance is obtained. In both cases, the remainders are expressed in terms of the third absolute moment of the additive function. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 74–80, January–March, 1999. Translated by A. Mačiulis 相似文献
17.
L. V. Rozovsky 《Acta Appl Math》1999,58(1-3):265-278
The objective of the paper is to study the asymptotic behavior of the reminder in the central limit theorem for moments of sums of independent random variables. 相似文献
18.
Gérard Ben Arous Marc Brunaud 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-4):79-144
This article concerns the asymptotic behaviour of diffusions consisting of various systems of mean-field type interacting particles. We specifically study the following properties: propagation of chaos; critical and non critical fluctuations, using the Laplace method which has been developed by Bolthausen in the general Banach valued random variables context; and finally the large deviations of laws of trajectorial empirical measures. We also study Gibbs variational formula associated with this problem and show that it reduces to a finite dimensional problem 相似文献
19.
We prove a local limit theorem (LLT) on Cramer-type large deviations for sums S
V
=
t
V (
t
), where
t
, t Z
, 1, is a Markov Gaussian random field, V Z
, and is a bounded Borel function. We get an estimate from below for the variance of S
V
and construct two classes of functions , for which the LLT of large deviations holds. 相似文献
20.
Examples of finite-dimensional structural design problems with constraints on natural frequency and buckling are used to demonstrate that repeated eigenvalues may be expected to occur when a structure is optimized. It is shown that a repeated eigenvalue is not generally differentiable with respect to design variables. Directional derivatives are shown to exist, and a method of calculating directional derivatives is given. Necessary conditions of optimality are derived and applied to a vibration optimization problem. Extensions of the theory to distributed-parameter structures and numerical methods are outlined.This research was supported by NSF Grant No. CMS-80-05677 相似文献