Random Matrix Theory and Wireless Communications

2004 ◽  
Vol 1 (1) ◽  
pp. 1-182 ◽  
Author(s):  
Antonia M. Tulino ◽  
Sergio Verdú
Keyword(s):  
Wireless Communications ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory

scholarly journals Large-dimensional random matrix theory and its applications in deep learning and wireless communications

2021 ◽  
pp. 2230001
Author(s):  
Jungang Ge ◽  
Ying-Chang Liang ◽  
Zhidong Bai ◽  
Guangming Pan
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Wireless Communications ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Communication Systems ◽  
Quantum Physics ◽  
Matrix Theory ◽  
Research Field ◽  
Analysis And Design

Large-dimensional (LD) random matrix theory, RMT for short, which originates from the research field of quantum physics, has shown tremendous capability in providing deep insights into large-dimensional systems. With the fact that we have entered an unprecedented era full of massive amounts of data and large complex systems, RMT is expected to play more important roles in the analysis and design of modern systems. In this paper, we review the key results of RMT and its applications in two emerging fields: wireless communications and deep learning. In wireless communications, we show that RMT can be exploited to design the spectrum sensing algorithms for cognitive radio systems and to perform the design and asymptotic analysis for large communication systems. In deep learning, RMT can be utilized to analyze the Hessian, input–output Jacobian and data covariance matrix of the deep neural networks, thereby to understand and improve the convergence and the learning speed of the neural networks. Finally, we highlight some challenges and opportunities in applying RMT to the practical large-dimensional systems.

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

Modeling of Integration Processes of Ukraine to EU Using Random Matrix Theory

2017 ◽  
Author(s):  
Hanna Danylchuk ◽  
Liubov Kibalnyk ◽  
Olexandr Serdiuk
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.

Random Matrix Theory for Analyzing Spatio-Temporal Data

2021 ◽  
pp. 144-174
Author(s):  
Robert Qiu ◽  
Xing He ◽  
Lei Chu ◽  
Xin Shi
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Temporal Data ◽  
Spatio Temporal
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