scholarly journals Non-gaussian non-hermitian random matrix theory: Phase transition and addition formalism

1997 ◽  
Vol 501 (3) ◽  
pp. 643-669 ◽  
Author(s):  
Joshua Feinberg ◽  
A. Zee
Keyword(s):  
Phase Transition ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Non Gaussian

scholarly journals KAPPA-DEFORMED RANDOM-MATRIX THEORY BASED ON KANIADAKIS STATISTICS

2012 ◽  
Vol 26 (10) ◽  
pp. 1250059 ◽  
Author(s):  
A. Y. ABUL-MAGD ◽  
M. ABDEL-MAGEED
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Distribution Functions ◽  
Spacing Distribution ◽  
Initial Stage ◽  
The Matrix ◽  
Gibbs Entropy ◽  
Non Gaussian ◽  
Mixed Systems

We present a possible extension of the random-matrix theory, which is widely used to describe spectral fluctuations of chaotic systems. By considering the Kaniadakis non-Gaussian statistics, characterized by the index κ (Boltzmann–Gibbs entropy is recovered in the limit κ → 0), we propose the non-Gaussian deformations (κ ≠ 0) of the conventional orthogonal and unitary ensembles of random matrices. The joint eigenvalue distributions for the κ-deformed ensembles are derived by applying the principle maximum entropy to Kaniadakis entropy. The resulting distribution functions are base invariant as they depend on the matrix elements in a trace form. Using these expressions, we introduce a new generalized form of the Wigner surmise valid for nearly-chaotic mixed systems, where a basis-independent description is still expected to hold. We motivate the necessity of such generalization by the need to describe the transition of the spacing distribution from chaos to order, at least in the initial stage. We show several examples about the use of the generalized Wigner surmise to the analysis of the results of a number of previous experiments and numerical experiments. Our results suggest the entropic index κ as a measure for deviation from the state of chaos. We also introduce a κ-deformed Porter–Thomas distribution of transition intensities, which fits the experimental data for mixed systems better than the commonly-used gamma-distribution.

scholarly journals Framework of Random Matrix Theory for Power System Data Mining in a Non-Gaussian Environment

IEEE Access ◽  
2016 ◽  
Vol 4 ◽  
pp. 9969-9977 ◽  
Author(s):  
Bei Han ◽  
Lingen Luo ◽  
Gehao Sheng ◽  
Guojie Li ◽  
Xiuchen Jiang
Keyword(s):  
Data Mining ◽  
Power System ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
System Data ◽  
Non Gaussian

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.

Sign in / Sign up

Export Citation Format

Share Document