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Random Matrix Theory and Its Applications
Statistical Science, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Random Matrix Theory and Wireless Communications
Foundations and Trends® in Communications and Information Theory, 2004Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic ...
Antonia M. Tulino, Sergio Verdú
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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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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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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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On Random Matrix Theory for stationary processes
2010 IEEE International Conference on Acoustics, Speech and Signal Processing, 2010Random Matrix Theory has generated tremendous interest in recent years, partly from powerful results developed for multi-user detection theory but also for growing applications in statistics, signal processing and econometrics. However the current theory has emphasized white noise data.
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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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On Random Matrix Theory and Autoregressive Modeling
2019 IEEE 58th Conference on Decision and Control (CDC), 2019Random matrix theory has attracted growing interest in signal processing and communications over the last one or two decades. It has gained further impetus due to the upsurge in the occurrence of ’big data’. However so far little of this interest has seeped into system identification.
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Test of the Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
Physical Review Letters, 2021Masahito Ueda +2 more
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