scholarly journals Lyapunov Spectra of Correlated Random Matrices

2000 ◽  
Vol 138 ◽  
pp. 592-593
Author(s):  
Tsuneyasu Okabe ◽  
Hiroaki Yamada
Keyword(s):  
Random Matrices ◽  
Lyapunov Spectra

Communication Optimal Parallel Multiplication of Sparse Random Matrices

2013 ◽  
Author(s):  
Grey Ballard ◽  
Aydin Buluc ◽  
James Demmel ◽  
Laura Grigori ◽  
Benjamin Lipshitz ◽  
...  
Keyword(s):  
Random Matrices ◽  
Sparse Random Matrices ◽  
Parallel Multiplication

VICTORIA transform, RESPECT and REFORM methods for the proof of the G-Elliptic Law under G-Lindeberg condition and twice stochastic condition for the variances and covariances of the entries of some random matrices

2020 ◽  
Vol 28 (2) ◽  
pp. 131-162
Author(s):  
Vyacheslav L. Girko
Keyword(s):  
Random Matrices ◽  
Random Matrix ◽  
Lindeberg Condition

AbstractThe G-Elliptic law under the G-Lindeberg condition for the independent pairs of the entries of a random matrix is proven.

scholarly journals How Many Inflections are There in the Lyapunov Spectrum?

2021 ◽  
Author(s):  
O. Jenkinson ◽  
M. Pollicott ◽  
P. Vytnova
Keyword(s):  
Piecewise Linear ◽  
Lyapunov Spectrum ◽  
Stat Phys ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Expanding Map ◽  
Lyapunov Spectra ◽  
Linear Maps ◽  
Inflection Points ◽  
Piecewise Linear Maps

AbstractIommi and Kiwi (J Stat Phys 135:535–546, 2009) showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this paper we answer a conjecture in Iommi and Kiwi (2009) by proving that the Lyapunov spectrum of a two branch piecewise linear map has at most two points of inflection. We then answer a question in Iommi and Kiwi (2009) by proving that there exist finite branch piecewise linear maps whose Lyapunov spectra have arbitrarily many points of inflection. This approach is used to exhibit a countable branch piecewise linear map whose Lyapunov spectrum has infinitely many points of inflection.

Diagrammatic Perturbation Expansion for Ensembles of Random Matrices

1970 ◽  
Vol 11 (10) ◽  
pp. 3103-3110 ◽  
Author(s):  
J. F. McDonald ◽  
L. D. Favro
Keyword(s):  
Random Matrices ◽  
Perturbation Expansion

scholarly journals Eigenvalues and Condition Numbers of Complex Random Matrices

2004 ◽  
Vol 26 (2) ◽  
pp. 441-456 ◽  
Author(s):  
T. Ratnarajah ◽  
R. Vaillancourt ◽  
M. Alvo
Keyword(s):  
Random Matrices ◽  
Condition Numbers
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