Results 61 to 70 of about 2,230,753 (183)
Singularity of random symmetric matrices – simple proof
Comptes Rendus. Mathématique, 2021 In this paper we give a simple, short, and self-contained proof for a non-trivial upper bound on the probability that a random $\pm 1$ symmetric matrix is singular.
Ferber, Asaf
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The Polynomial Method for Random Matrices [PDF]
Foundations of Computational Mathematics, 2007 We define a class of "algebraic" random matrices. These are random matrices for which the Stieltjes transform of the limiting eigenvalue distribution function is algebraic, i.e., it satisfies a (bivariate) polynomial equation. The Wigner and Wishart matrices whose limiting eigenvalue distributions are given by the semi-circle law and the Marcenko ...
N. Raj Rao, Alan Edelman
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Wilson loops and random matrices
Journal of High Energy PhysicsLinear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices.
Georg Bergner +3 more
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, 2023 Random Matrix theory has become a field on its own with a breadth of new results, techniques, and ideas in the last thirty years. In these proceedings of the 8ECM 2021, I illustrate some of these advances by describing what is known about the spectrum and the eigenvectors of Bernoulli matrices.
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Fast and efficient compressive sensing using structurally random matrices [PDF]
, 2012 This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2011 IEEE. Personal use of this material is permitted.
Trac D. Tran +7 more
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Level Compressibility of Certain Random Unitary Matrices
Entropy, 2022 The value of spectral form factor at the origin, called level compressibility, is an important characteristic of random spectra. The paper is devoted to analytical calculations of this quantity for different random unitary matrices describing models with
Eugene Bogomolny
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The random phase property and the Lyapunov Spectrum for disordered multi-channel systems [PDF]
, 2010 A random phase property establishing in the weak coupling limit a link between quasi-one-dimensional random Schrödinger operators and full random matrix theory is advocated.
Römer, Rudolf A., Schulz-Baldes, H.
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On the Singularity of Random Combinatorial Matrices [PDF]
SIAM Journal on Discrete Mathematics, 2013 It is shown that a random $(0,1)$ matrix whose rows are independent random vectors of exactly $n/2$ zero components is non-singular with probability $1-O(n^{-C})$ for any $C>0$. The proof uses a non-standard inverse-type Littlewood-Offord result.
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Characteristic polynomials of complex random matrix models [PDF]
, 2002 We calculate the expectation value of an arbitrary product of characteristic polynomials of complex random matrices and their hermitian conjugates. Using the technique of orthogonal polynomials in the complex plane our result can be written in terms of
Akemann, G +3 more
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