Random Matrix Theory and Maximum Entropy Models for Disordered Conductors

1991 ◽  
pp. 369-448 ◽  
Author(s):  
A. Douglas STONE ◽  
Pier A. MELLO ◽  
Khandker A. MUTTALIB ◽  
Jean-Louis PICHARD
Keyword(s):  
Maximum Entropy ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Maximum Entropy Models

scholarly journals A MODEL OF TWO-DIMENSIONAL TURBULENCE USING RANDOM MATRIX THEORY

2002 ◽  
Vol 17 (23) ◽  
pp. 1539-1550 ◽  
Author(s):  
SAVITRI V. IYER ◽  
S. G. RAJEEV
Keyword(s):  
Maximum Entropy ◽  
Random Matrices ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Simple Formula ◽  
Matrix Theory ◽  
Inviscid Flow ◽  
Two Dimensional ◽  
Cylindrically Symmetric ◽  
Vortex Field

We derive a formula for the entropy of two-dimensional incompressible inviscid flow, by determining the volume of the space of vorticity distributions with fixed values for the moments Qk = ∫ ω(x)kd2x. This space is approximated by a sequence of spaces of finite volume, by using a regularization of the system that is geometrically natural and connected with the theory of random matrices. By taking the limit we get a simple formula for the entropy of a vortex field. We predict vorticity distributions of maximum entropy with given mean vorticity and enstrophy; we also predict the cylindrically symmetric vortex field with maximum entropy. This could be an approximate description of a hurricane.

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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