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A First Course in Random Matrix Theory
, 2020The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of ...
M. Potters, J. Bouchaud
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2017
Random matrix theory deals with the study of matrix-valued random variables. It is conventionally considered that random matrix theory dates back to the work of Wishart in 1928 [1] on the properties of matrices of the type XX † with X ε ℂ N×n a random matrix with independent Gaussian entries with zero mean and equal variance.
Couillet, Romain, Debbah, Merouane
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Random matrix theory deals with the study of matrix-valued random variables. It is conventionally considered that random matrix theory dates back to the work of Wishart in 1928 [1] on the properties of matrices of the type XX † with X ε ℂ N×n a random matrix with independent Gaussian entries with zero mean and equal variance.
Couillet, Romain, Debbah, Merouane
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Complex Market Dynamics in the Light of Random Matrix Theory
New Economic Windows, 2018We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems.
Hirdesh K. Pharasi +3 more
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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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Superanalysis for Random-Matrix Theory [PDF]
, 2001 Gossip has it that the “supersymmetry technique” is difficult to learn. But quite to the contrary, representing determinants as Gaussian integrals over anticommuting alias Grassmann variables makes for great simplifications in computing averages over the underlying matrices, as we have seen in Chaps. 4 and 8. Even in the semiclassical work of Chap.
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Bifurcations and random matrix theory
Europhysics Letters (EPL), 2001The divergence of semiclassical amplitudes at periodic orbit bifurcations has strong effects on long-range spectral statistics. We discuss the statistical weight of such effects in parameter space, using as an example the quantised standard map as a function of the kicking strength.
Peter Pollner, Bruno Eckhardt
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Random Matrix Theory and Wireless Communications
Foundations and Trends in Communications and Information Theory, 2004A. Tulino, S. Verdú
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Random matrix theory and the scaling theory of localization
Physical Review Letters, 1990We consider the most probable value of conductance of a disordered quantum conductor in the framework of the random matrix theory developed earlier. Analytic calculations are possible in the metallic as well as strongly localized regimes. We make a simple assumption on the eigenvalue density, as suggested by numerical work, and explore the consequences
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