scholarly journals Eigenvalue distribution of some nonlinear models of random matrices

2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Lucas Benigni ◽  
Sandrine Péché
Keyword(s):  
Random Matrices ◽  
Nonlinear Models ◽  
Eigenvalue Distribution

The smallest eigenvalue distribution at the spectrum edge of random matrices

1998 ◽  
Vol 509 (3) ◽  
pp. 561-598 ◽  
Author(s):  
Taro Nagao ◽  
Peter J. Forrester
Keyword(s):  
Random Matrices ◽  
Eigenvalue Distribution ◽  
Smallest Eigenvalue

scholarly journals Limiting spectral distributions of sums of products of non-Hermitian random matrices

2018 ◽  
Vol 38 (2) ◽  
pp. 359-384
Author(s):  
Holger Kösters ◽  
Alexander Tikhomirov
Keyword(s):  
Probability Theory ◽  
Random Matrices ◽  
General Framework ◽  
Free Probability ◽  
Singular Value ◽  
Eigenvalue Distribution ◽  
Limiting Distributions ◽  
Free Probability Theory ◽  
Spectral Distributions ◽  
Sums Of Products

For fixed l≥0 and m≥1, let Xn0, Xn1,..., Xnl be independent random n × n matrices with independent entries, let Fn0 := Xn0, Xn1-1,..., Xnl-1, and let Fn1,..., Fnm be independent random matrices of the same form as Fn0 . We show that as n → ∞, the matrices Fn0 and m−l+1/2Fn1 +...+ Fnm have the same limiting eigenvalue distribution. To obtain our results, we apply the general framework recently introduced in Götze, Kösters, and Tikhomirov 2015 to sums of products of independent random matrices and their inverses.We establish the universality of the limiting singular value and eigenvalue distributions, and we provide a closer description of the limiting distributions in terms of free probability theory.

Eigenvalue Distribution of Large Random Matrices

2011 ◽  
Author(s):  
Leonid Pastur ◽  
Mariya Shcherbina
Keyword(s):  
Random Matrices ◽  
Eigenvalue Distribution

scholarly journals Eigenvalue distribution of large dilute random matrices

1997 ◽  
Vol 38 (6) ◽  
pp. 3300-3320 ◽  
Author(s):  
A. Khorunzhy ◽  
G. J. Rodgers
Keyword(s):  
Random Matrices ◽  
Eigenvalue Distribution

scholarly journals Measuring maximal eigenvalue distribution of Wishart random matrices with coupled lasers

2012 ◽  
Vol 85 (2) ◽  
Author(s):  
Moti Fridman ◽  
Rami Pugatch ◽  
Micha Nixon ◽  
Asher A. Friesem ◽  
Nir Davidson
Keyword(s):  
Random Matrices ◽  
Eigenvalue Distribution ◽  
Maximal Eigenvalue ◽  
Coupled Lasers

scholarly journals Progress on Complex Langevin simulations of a finite density matrix model for QCD

2018 ◽  
Vol 175 ◽  
pp. 07034
Author(s):  
Jacques Bloch ◽  
Jonas Glesaaen ◽  
Jacobus Verbaarschot ◽  
Savvas Zafeiropoulos
Keyword(s):  
Density Matrix ◽  
Detailed Analysis ◽  
Time Evolution ◽  
Random Matrices ◽  
Matrix Model ◽  
Substantial Improvement ◽  
Eigenvalue Distribution ◽  
Finite Density

We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to intended theory with dynamical quarks. A detailed analysis of this issue and a potential resolution of the failure of this algorithm are discussed. We study the effect of gauge cooling on the Dirac eigenvalue distribution and time evolution of the norm for various cooling norms, which were specifically designed to remove the pathologies of the complex Langevin evolution. The cooling is further supplemented with a shifted representation for the random matrices. Unfortunately, none of these modifications generate a substantial improvement on the complex Langevin evolution and the final results still do not agree with the analytical predictions.

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