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Doklady Mathematics - We consider sparse sample covariance matrices with sparsity probability $${{p}_{n}} \geqslant {{c}_{0}}{{\log }^{{\frac{2}{\varkappa }}}}n{\text{/}}n$$ with $$\varkappa... 相似文献
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Friedrich Götze Alexander N. Tikhomirov Dmitry A. Timushev 《Central European Journal of Mathematics》2007,5(2):305-334
It is shown that the Kolmogorov distance between the expected spectral distribution function of an n × n matrix from the Deformed Gaussian Ensemble and the distribution function of the semi-circle law is of order O(n
−2/3+v
).
Research supported by the DFG-Forschergruppe FOR 399/1. Partially supported by INTAS grant N 03-51-5018, by RFBF grant N 02-01-00233,
by RFBR-DFG grant N 04-01-04000, by RF grant of the leading scientific schools NSh-4222.2006.1. 相似文献
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Current approaches to fan noise simulation are mainly based on the Lighthill equation and socalled aeroacoustic analogy, which are also based on the transformed Lighthill equation, such as the wellknown FW-H equation or the Kirchhoff theorem. A disadvantage of such methods leading to significant modeling errors is associated with incorrect solution of the decomposition problem, i.e., separation of acoustic and vortex (pseudosound) modes in the area of the oscillation source. In this paper, we propose a method for tonal noise simulation based on the mesh solution of the Helmholtz equation for the Fourier transform of pressure perturbation with boundary conditions in the form of the complex impedance. A noise source is placed on the surface surrounding each fan rotor. The acoustic fan power is determined by the acoustic-vortex method, which ensures more accurate decomposition and determination of the pressure pulsation amplitudes in the near field of the fan. 相似文献
4.
Symmetric random matrices are considered whose upper triangular entries are independent identically distributed random variables with zero mean, unit variance, and a finite moment of order 4 + δ, δ > 0. It is shown that the distances between the Stieltjes transforms of the empirical spectral distribution function and the semicircle law are of order lnn/nv, where v is the distance to the real axis in the complex plane. Applications concerning the convergence rate in probability to the semicircle law, localization of eigenvalues, and delocalization of eigenvectors are discussed. 相似文献
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