Results 51 to 60 of about 2,230,753 (183)
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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Free random Lévy matrices [PDF]
Physical Review E, 2002 Using the theory of free random variables (FRV) and the Coulomb gas analogy, we construct stable random matrix ensembles that are random matrix generalizations of the classical one-dimensional stable Lévy distributions. We show that the resolvents for the corresponding matrices obey transcendental equations in the large size limit.
Burda, Z. +5 more
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Universality classes of non-Hermitian random matrices
Physical Review Research, 2020 Non-Hermitian random matrices have been utilized in such diverse fields as dissipative and stochastic processes, mesoscopic physics, nuclear physics, and neural networks.
Ryusuke Hamazaki +3 more
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Modern Stochastics: Theory and Applications, 2022 The generalised sine random point field arises from the scaling limit at the origin of the eigenvalues of the generalised Gaussian ensembles. We solve an infinite-dimensional stochastic differential equation (ISDE) describing an infinite number of ...
Yosuke Kawamoto
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Stieltjes Transforms and R-Transforms Associated with Two-Parameter Lambert–Tsallis Functions
Entropy, 2023 In this paper, we study a two-parameter family of Stieltjes transformations related to holomorphic Lambert–Tsallis functions, which are a two-parameter generalization of the Lambert function.
Hideto Nakashima, Piotr Graczyk
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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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Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations
Risks, 2018 We review recent progress in modeling credit risk for correlated assets. We employ a new interpretation of the Wishart model for random correlation matrices to model non-stationary effects.
Andreas Mühlbacher, Thomas Guhr
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Independence Characterization for Wishart and Kummer Random Matrices
Revstat Statistical Journal, 2020 We generalize the following univariate characterization of the Kummer and Gamma distributions to the cone of symmetric positive definite matrices: let X and Y be independent, non-degenerate random variables valued in (0,∞), then U = Y /(1 +X) and V = X ...
Bartosz Ko lodziejek +1 more
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Characteristic Polynomials of Random Matrices [PDF]
Communications in Mathematical Physics, 2000 Number theorists have studied extensively the connections between the distribution of zeros of the Riemann $ζ$-function, and of some generalizations, with the statistics of the eigenvalues of large random matrices. It is interesting to compare the average moments of these functions in an interval to their counterpart in random matrices, which are the ...
Brezin, E., Hikami, S.
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Limit Theorems for Spectra of Circulant Block Matrices with Large Random Blocks
MathematicsThis paper investigates the spectral properties of block circulant matrices with high-order symmetric (or Hermitian) blocks. We analyze cases with dependent or sparse independent entries within these blocks.
Alexander Tikhomirov +2 more
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