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Applied Mathematics and Computation, 2007
This work is concerned with the numerical rank of matrix in the matrix computations. We conclude that a real random matrix has full rank with probability 1 and a rational random matrix has full rank with probability 1 too. Finally, the applications of the numerical matrix are given.
Xinlong Feng, Xinlong Feng, Zhinan Zhang
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This work is concerned with the numerical rank of matrix in the matrix computations. We conclude that a real random matrix has full rank with probability 1 and a rational random matrix has full rank with probability 1 too. Finally, the applications of the numerical matrix are given.
Xinlong Feng, Xinlong Feng, Zhinan Zhang
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1992
Before about 1956, there was no systematic statistical theory of nuclear energy level structure. There was a shortage of close spacings in experimentally obtained energy levels which was generally dismissed as being due to instrumental resolution failings.
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Before about 1956, there was no systematic statistical theory of nuclear energy level structure. There was a shortage of close spacings in experimentally obtained energy levels which was generally dismissed as being due to instrumental resolution failings.
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2001
A wealth of empirical and numerical evidence suggests universality for local fluctuations in quantum energy or quasi-energy spectra of systems that display global chaos in their classical phase spaces. Exceptions apart, all such Hamiltonian matrices of sufficiently large dimension yield the same spectral fluctuations provided they have the same group ...
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A wealth of empirical and numerical evidence suggests universality for local fluctuations in quantum energy or quasi-energy spectra of systems that display global chaos in their classical phase spaces. Exceptions apart, all such Hamiltonian matrices of sufficiently large dimension yield the same spectral fluctuations provided they have the same group ...
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2004
In this chapter, we will work not with \(\mathrm{GL}(n, \mathbb{C})\) but with its compact subgroup U(n). As in the previous chapters, we will consider elements of \(\mathcal{R}_{k}\) as generalized characters on S k . If \(\mathbf{f} \in \mathcal{R}_{k}\), then \(f ={ \mathrm{ch}}^{(n)}(\mathbf{f}) \in \varLambda _{k}^{(n)}\) is a symmetric polynomial
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In this chapter, we will work not with \(\mathrm{GL}(n, \mathbb{C})\) but with its compact subgroup U(n). As in the previous chapters, we will consider elements of \(\mathcal{R}_{k}\) as generalized characters on S k . If \(\mathbf{f} \in \mathcal{R}_{k}\), then \(f ={ \mathrm{ch}}^{(n)}(\mathbf{f}) \in \varLambda _{k}^{(n)}\) is a symmetric polynomial
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AIP Conference Proceedings, 2006
We have performed a study of the statistical mechanics of correlated spectra first introduced by Dyson and Mehta some 40 years ago. We have derived a modified thermodynamical statistics (a number and its variance) for linear spectra. This approach was used to analyze the statistical properties of the eigenvalues of random matrices of Gaussian ensembles
Alberto Tufaile +4 more
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We have performed a study of the statistical mechanics of correlated spectra first introduced by Dyson and Mehta some 40 years ago. We have derived a modified thermodynamical statistics (a number and its variance) for linear spectra. This approach was used to analyze the statistical properties of the eigenvalues of random matrices of Gaussian ensembles
Alberto Tufaile +4 more
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Matrix realization of random surfaces
Physical Review D, 1991The large-N one-matrix model with a potential V(φ)=φ 2 /2+g 4 φ 4 /N+g 6 φ 6 /N 2 is carefully investigated using the orthogonal polynomial method. We present a numerical method to solve the recurrence relation and evaluate the recursion coefficients r k (k=1,2,3,...) of the orthogonal polynomials at large N.
Hiroshi Suzuki +2 more
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2013
This chapter presents algorithms for uniform matrix sample generation in norm-bounded sets. First, we discuss the simple case of matrix sampling in sets defined by l p Hilbert–Schmidt norm, which reduces to the vector l p norm randomization problem. Subsequently, we present an efficient solution to the problem of uniform generation in sets defined by ...
Giuseppe Carlo Calafiore +2 more
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This chapter presents algorithms for uniform matrix sample generation in norm-bounded sets. First, we discuss the simple case of matrix sampling in sets defined by l p Hilbert–Schmidt norm, which reduces to the vector l p norm randomization problem. Subsequently, we present an efficient solution to the problem of uniform generation in sets defined by ...
Giuseppe Carlo Calafiore +2 more
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The Lowest Eigenvalue of a Random Matrix
SIAM Journal on Applied Mathematics, 1980The first few moments of the distribution of the top eigenvalue of a discrete version of the operator $ - \nabla ^2 + q$ determine the mean of the random potential q up to a finite number of choices.
F. Alberto Grünbaum, John T. Antoun
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Perturbations of random matrix products
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1982If X1, X2,... are identically distributed independent random matrices with a common distribution μ then with the probability 1 the limit $$\Lambda _\mu = \mathop {\lim }\limits_{n \to \infty } \frac{1}{n}\ln \left\| {X_n ...X_1 } \right\|$$ exists. The paper treats the problem: is it true that Λµk→Λµ if µk→µ in the weak sense?
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