Results 31 to 40 of about 182,487 (307)
Black holes and random matrices
Journal of High Energy Physics, 2017 We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems.
Jordan S. Cotler +8 more
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A note on the tensor product of two random unitary matrices [PDF]
, 2013 In this note we consider the point process of eigenvalues of the tensor product of two independent random unitary matrices of size m x m and n x n. When n becomes large, the process behaves like the superposition of m independent sine processes.
Tkocz, Tomasz
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Relating Entropies of Quantum Channels
Entropy, 2021 In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state.
Dariusz Kurzyk +2 more
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Generalized Ensemble of Random Matrices [PDF]
Physical Review Letters, 1994 9 ...
Moshe, Moshe +2 more
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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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The Full Rank Condition for Sparse Random Matrices [PDF]
, 2023 We derive a sufficient condition for a sparse random matrix with given numbers of non-zero entries in the rows and columns having full row rank. Inspired by low-density parity check codes, the family of random matrices that we investigate is very general
Rolvien, Maurice +6 more
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A Note on Cumulant Technique in Random Matrix Theory
Entropy, 2023 We discuss the cumulant approach to spectral properties of large random matrices. In particular, we study in detail the joint cumulants of high traces of large unitary random matrices and prove Gaussian fluctuation for pair-counting statistics with non ...
Alexander Soshnikov, Chutong Wu
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On the Rank of Random Sparse Matrices [PDF]
Combinatorics, Probability and Computing, 2009 We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This allows us to obtain an exact estimate for the co-rank.
Kevin P. Costello, Van H. Vu
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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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Eigenvalue distributions of beta-Wishart matrices [PDF]
, 2018 We derive explicit expressions for the distributions of the extreme eigenvalues of the Beta-Wishart random matrices in terms of the hypergeometric function of a matrix argument. These results generalize the classical results for the real (β = 1), complex
Koev, Plamen S, Edelman, Alan
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