scholarly journals Level statistics inside the vortex of a superconductor and symplectic random-matrix theory in an external source

1999 ◽  
Vol 60 (5) ◽  
pp. 3589-3602 ◽  
Author(s):  
E. Brézin ◽  
S. Hikami ◽  
A. I. Larkin
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
External Source ◽  
Level Statistics

Random matrix representations of critical statistics

2018 ◽  
Author(s):  
Alexei Borodin
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Luttinger Liquid ◽  
Matrix Representations ◽  
Level Statistics ◽  
Random Matrix Models ◽  
Matrix Ensemble ◽  
Spectral Statistics ◽  
Random Matrix Ensembles

This article examines two random matrix ensembles that are useful for describing critical spectral statistics in systems with multifractal eigenfunction statistics: the Gaussian non-invariant ensemble and the invariant random matrix ensemble. It first provides an overview of non-invariant Gaussian random matrix theory (RMT) with multifractal eigenvectors and invariant random matrix theory (RMT) with log-square confinement before discussing self-unfolding and not self-unfolding in invariant RMT. It then considers a non-trivial unfolding and how it changes the form of the spectral correlations, along with the appearance of a ghost correlation dip in RMT and Hawking radiation. It also describes the correspondence between invariant and non-invariant ensembles and concludes by introducing a simple field theory in 1+1 dimensions which reproduces level statistics of both of the two random matrix models and the classical Wigner-Dyson spectral statistics in the framework of the unified formalism of Luttinger liquid.

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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