Gaussian point processes and two-by-two random matrix theory

2007 ◽  
Vol 76 (4) ◽  
Author(s):  
John M. Nieminen
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Point Processes ◽  
Matrix Theory ◽  
Gaussian Point

The Oxford Handbook of Random Matrix Theory

2018 ◽  
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Point Processes ◽  
Matrix Theory ◽  
Fundamental Property ◽  
Mathematical Concept ◽  
Determinantal Point Processes ◽  
Classical Orthogonal Polynomials ◽  
Symmetry Classes ◽  
Finite Matrix

This handbook showcases the major aspects and modern applications of random matrix theory (RMT). It examines the mathematical properties and applications of random matrices and some of the reasons why RMT has been very successful and continues to enjoy great interest among physicists, mathematicians and other scientists. It also discusses methods of solving RMT, basic properties and fundamental objects in RMT, and different models and symmetry classes in RMT. Topics include the use of classical orthogonal polynomials (OP) and skew-OP to solve exactly RMT ensembles with unitary, and orthogonal or symplectic invariance respectively, all at finite matrix size; the supersymmetric and replica methods; determinantal point processes; Painlevé transcendents; the fundamental property of RMT known as universality; RNA folding; two-dimensional quantum gravity; string theory; and the mathematical concept of free random variables. In addition to applications to mathematics and physics, the book considers broader applications to other sciences, including economics, engineering, biology, and complex networks.

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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