scholarly journals Matrix Product States, Random Matrix Theory and the Principle of Maximum Entropy

2013 ◽  
Vol 320 (3) ◽  
pp. 663-677 ◽  
Author(s):  
Benoît Collins ◽  
Carlos E. González-Guillén ◽  
David Pérez-García
Keyword(s):  
Maximum Entropy ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Matrix Product ◽  
Matrix Product States ◽  
Principle Of Maximum Entropy ◽  
Principle Of Maximum

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.

scholarly journals To Be or to Have Been Lucky, That Is the Question

Philosophies ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 57
Author(s):  
Antony Lesage ◽  
Jean-Marc Victor
Keyword(s):  
High Risk ◽  
Maximum Entropy ◽  
Chronic Diseases ◽  
Statistical Test ◽  
Low Risk ◽  
Principle Of Maximum Entropy ◽  
Ex Ante ◽  
Social Opportunities ◽  
Global Population ◽  
Principle Of Maximum

Is it possible to measure the dispersion of ex ante chances (i.e., chances “before the event”) among people, be it gambling, health, or social opportunities? We explore this question and provide some tools, including a statistical test, to evidence the actual dispersion of ex ante chances in various areas, with a focus on chronic diseases. Using the principle of maximum entropy, we derive the distribution of the risk of becoming ill in the global population as well as in the population of affected people. We find that affected people are either at very low risk, like the overwhelming majority of the population, but still were unlucky to become ill, or are at extremely high risk and were bound to become ill.

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