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141.
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   
142.
Carl  Bernd  Defant  Andreas 《Positivity》2000,4(2):131-141
A celebrated result of Johnson, Maurey, König and Retherford from 1977 states that for every complex matrix satisfies the following eigenvalue estimate:
Based on the concept of entropy numbers and a simple product trick we give a selfcontained elementary proof.  相似文献   
143.
144.
The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in the TASEP with the step initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of the TASEP to the Schur process, we show that the function is represented as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources.  相似文献   
145.
We consider a system of diffusing particles on the real line in a quadratic external potential and with a logarithmic interaction potential. The empirical measure process is known to converge weakly to a deterministic measure-valued process as the number of particles tends to infinity. Provided the initial fluctuations are small, the rescaled linear statistics of the empirical measure process converge in distribution to a Gaussian limit for sufficiently smooth test functions. For a large class of analytic test functions, we derive explicit general formulae for the mean and covariance in this central limit theorem by analyzing a partial differential equation characterizing the limiting fluctuations.  相似文献   
146.
The main issue we address in the present paper are the new models for completely nonunitary contractions with rank one defect operators acting on some Hilbert space of dimension N?∞. These models complement nicely the well-known models of Livšic and Sz.-Nagy-Foias. We show that each such operator acting on some finite-dimensional (respectively, separable infinite-dimensional Hilbert space) is unitarily equivalent to some finite (respectively semi-infinite) truncated CMV matrix obtained from the “full” CMV matrix by deleting the first row and the first column, and acting in CN (respectively ?2(N)). This result can be viewed as a nonunitary version of the famous characterization of unitary operators with a simple spectrum due to Cantero, Moral and Velázquez, as well as an analog for contraction operators of the result from [Yu. Arlinski?, E. Tsekanovski?, Non-self-adjoint Jacobi matrices with a rank-one imaginary part, J. Funct. Anal. 241 (2006) 383-438] concerning dissipative non-self-adjoint operators with a rank one imaginary part. It is shown that another functional model for contractions with rank one defect operators takes the form of the compression f(ζ)→PK(ζf(ζ)) on the Hilbert space L2(T,dμ) with a probability measure μ onto the subspace K=L2(T,dμ)?C. The relationship between characteristic functions of sub-matrices of the truncated CMV matrix with rank one defect operators and the corresponding Schur iterates is established. We develop direct and inverse spectral analysis for finite and semi-infinite truncated CMV matrices. In particular, we study the problem of reconstruction of such matrices from their spectrum or the mixed spectral data involving Schur parameters. It is pointed out that if the mixed spectral data contains zero eigenvalue, then no solution, unique solution or infinitely many solutions may occur in the inverse problem for truncated CMV matrices. The uniqueness theorem for recovered truncated CMV matrix from the given mixed spectral data is established. In this part the paper is closely related to the results of Hochstadt and Gesztesy-Simon obtained for finite self-adjoint Jacobi matrices.  相似文献   
147.
Let D be a division ring with an involution-,H2(D) be the set of 2 × 2 Hermitian matrices over D. Let ad(A,B) = rank(A-B) be the arithmetic distance between A,B ∈ H2(D) . In this paper,the fundamental theorem of the geometry of 2 × 2 Hermitian matrices over D(char(D) = 2) is proved:if  :H2(D) → H2(D) is the adjacency preserving bijective map,then  is of the form (X) = tP XσP +(0) ,where P ∈ GL2(D) ,σ is a quasi-automorphism of D. The quasi-automorphism of D is studied,and further results are obtained.  相似文献   
148.
There is remarkable and distinctive structure among Hermitian matrices, whose graph is a given tree T and that have an eigenvalue of multiplicity that is a maximum for T. Among such structure, we give several new results: (1) no vertex of T may be “neutral”; (2) neutral vertices may occur if the largest multiplicity is less than the maximum; (3) every Parter vertex has at least two downer branches; (4) removal of a Parter vertex changes the status of no other vertex; and (5) every set of Parter vertices forms a Parter set. Statements (3), (4) and (5) are also not generally true when the multiplicity is less than the maximum. Some of our results are used to give further insights into prior results, and both the review of necessary background and the development of new structural lemmas may be of independent interest.  相似文献   
149.
A brief account of the conceptual formulation of the two entities in this paper’s title, plus an initial preliminary investigation of some of their mathematical properties, is given.  相似文献   
150.
A different approach is given to recent results due mainly to R. C. Johnson and A. Leal Duarte on the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree. The techniques developed are based on some results of matching polynomials and used a work by O. L. Heilmann and E. H. Lieb on an apparently unrelated topic.   相似文献   
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