Random matrix theory model for mean notch depth of the diagonally loaded minimum variance distortionless response beamformer for a single interferer case

2014 ◽  
Vol 135 (4) ◽  
pp. 2359-2359
Author(s):  
Saurav R. Tuladhar ◽  
John R. Buck ◽  
Kathleen E. Wage
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Minimum Variance ◽  
Theory Model ◽  
Notch Depth ◽  
Minimum Variance Distortionless Response

The Riemann zeta-function and moment conjectures from Random Matrix Theory

2009 ◽  
Vol 59 (3) ◽  
Author(s):  
Jörn Steuding
Keyword(s):  
Zeta Function ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Riemann Zeta Function ◽  
Matrix Theory ◽  
Limited Range ◽  
Theory Model ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Discrete Moments

AbstractOn the basis of the Random Matrix Theory-model several interesting conjectures for the Riemann zeta-function were made during the recent past, in particular, asymptotic formulae for the 2kth continuous and discrete moments of the zeta-function on the critical line, $$ \frac{1} {T}\int\limits_0^T {|\zeta (\tfrac{1} {2} + it)|^{2k} dt} and \frac{1} {{N(T)}}\sum\limits_{0 < \gamma \leqslant {\rm T}} {|\zeta (\tfrac{1} {2} + i(\gamma + \tfrac{\alpha } {L}))|^{2k} } $$, by Conrey, Keating et al. and Hughes, respectively. These conjectures are known to be true only for a few values of k and, even under assumption of the Riemann hypothesis, estimates of the expected order of magnitude are only proved for a limited range of k. We put the discrete moment for k = 1, 2 in relation with the corresponding continuous moment for the derivative of Hardy’s Z-function. This leads to upper bounds for the discrete moments which are off the predicted order by a factor of log T.

SSA, Random Matrix Theory, and Noise-Reduced Correlations

2016 ◽  
Author(s):  
Jan W Dash ◽  
Xipei Yang ◽  
Mario Bondioli ◽  
Harvey J. Stein
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory

History—an overview

2018 ◽  
Author(s):  
Oriol Bohigas ◽  
Hans A. Weidenmüller
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Rapid Development ◽  
The Past ◽  
History Of ◽  
And Mathematics

An overview of the history of random matrix theory (RMT) is provided in this chapter. Starting from its inception, the authors sketch the history of RMT until about 1990, focusing their attention on the first four decades of RMT. Later developments are partially covered. In the past 20 years RMT has experienced rapid development and has expanded into a number of areas of physics and mathematics.

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