Results 211 to 220 of about 128,402 (249)
Riemann Zeros and Random Matrix Theory [PDF]
Milan Journal of Mathematics, 2010 This is a survey article on the interaction between zeta functions and random matrix theory. Their connection originates from \textit{H. L. Montgomery}'s pair-correlation conjecture [in: Analytic Number Theory, Proc. Sympos. Pure Math. 24, 181--193 (1973; Zbl 0268.10023)], from which the story starts.
N C Snaith
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2016
In this chapter the Gaussian random matrix ensembles are investigated. We determine their Green’s functions and show that for small energy differences a soft mode appears. As a consequence, the non-linear sigma-model is introduced and the level correlations are determined.
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In this chapter the Gaussian random matrix ensembles are investigated. We determine their Green’s functions and show that for small energy differences a soft mode appears. As a consequence, the non-linear sigma-model is introduced and the level correlations are determined.
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Acta Numerica, 2005
Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else.
Alan Edelman, N. Raj Rao
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Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else.
Alan Edelman, N. Raj Rao
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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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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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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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RANDOM MATRIX THEORY AND FINANCIAL CORRELATIONS
International Journal of Theoretical and Applied Finance, 2000We show that results from the theory of random matrices are potentially of great interest when trying to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate financial time series. We find a remarkable agreement between the theoretical prediction (based on the assumption that the correlation
Laloux, Laurent +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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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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