Eigenvalue correlations for banded matrices
نویسندگان
چکیده
منابع مشابه
Eigenvalue Correlations for Banded Matrices
We study the evolution of the distribution of eigenvalues of a N × N matrix ensemble subject to a change of variances of its matrix elements. Our results indicate that the evolution of the probability density is governed by a Fokker-Planck equation similar to the one governing the time-evolution of the particle-distribution in Wigner-Dyson gas, with relative variances now playing the role of ti...
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We consider eigenvalue problems for self-adjoint Sturm-Liouville difference equations of any even order. It is well known that such problems with Dirichlet boundary conditions can be transformed into an algebraic eigenvalue problem for a banded, real-symmetric matrix, and vice versa. In this article it is shown that such a transform exists for general separated, self-adjoint boundary conditions...
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AproductADF1 : : : FN of invertible block-diagonalmatrices will be bandedwith a banded inverse. We establish this factorization with the numberN controlled by the bandwidthsw and not by the matrix size n:When A is an orthogonal matrix, or a permutation, or banded plus finite rank, the factors Fi have w D 1 and generate that corresponding group. In the case of infinite matrices, conjectures rema...
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Cβ(N) is a normalisation constant, w (z, z̄) is a weight function (see discussion below). For real matrices (β = 1) with no further symmetries, the reader is referred to much later papers by Lehmann and Sommers (1991), and also by Edelman (1997). Although Ginibre’s derivation of Eqs. (1) and (2) holds for random matrices with Gaussian distributed entries, that is for w(z, z̄) = w 0(z, z̄) = e , (3)
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We study the limiting eigenvalue distribution of n×n banded Toeplitz matrices as n → ∞. From classical results of Schmidt-Spitzer and Hirschman it is known that the eigenvalues accumulate on a special curve in the complex plane and the normalized eigenvalue counting measure converges weakly to a measure on this curve as n → ∞. In this paper, we characterize the limiting measure in terms of an e...
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ژورنال
عنوان ژورنال: Physica E: Low-dimensional Systems and Nanostructures
سال: 2001
ISSN: 1386-9477
DOI: 10.1016/s1386-9477(00)00261-7