Results 71 to 80 of about 2,230,753 (183)
Proceedings of the International Congress of Mathematicians (ICM 2018), 2019 We survey recent mathematical results about the spectrum of random band matrices. We start by exposing the Erd{\H o}s-Schlein-Yau dynamic approach, its application to Wigner matrices, and extension to other mean-field models. We then introduce random band matrices and the problem of their Anderson transition.
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Note on Matrices of Random Numbers
Psychological Reports, 2000 The statistical and structural characteristics of 13 matrices of random numbers in which both the cells and the entries were randomly chosen are discussed. Each matrix was explored considering row means, standard deviations, and correlations as well as column means, standard deviations, and correlations. A study concerning the sequential arrangement of
Rimoldi, Horacio J. A. +3 more
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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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The Expected Norm of Random Matrices [PDF]
Combinatorics, Probability and Computing, 2000 We compare the Euclidean operator norm of a random matrix with the Euclidean norm of its rows and columns. In the first part of this paper, we show that if A is a random matrix with i.i.d. zero mean entries, then E∥A∥h [les ] Kh (E maxi ∥ai[bull ] ∥h + E maxj ∥aj[bull ] ∥h), where K is a constant which does not depend on the dimensions or ...
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Realistic Many-Body Quantum Systems vs. Full Random Matrices: Static and Dynamical Properties
Entropy, 2016 We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos.
Eduardo Jonathan Torres-Herrera +3 more
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Random matrices: Probability of normality
Advances in Mathematics, 2019 In this paper, we investigate the following question: How often is a random matrix normal? We consider a random $n\times n$ matrix, $M_n$, whose entries are i.i.d. Rademacher random variables (taking values $\{ \pm1 \}$ with probability $1/2$) and prove $$2^{-\left(0.5+o(1)\right)n^2} \le P\left(M_n \text{ is normal}\right) \le 2^{-(0.302+o(1))n^{2}}. $
Deneanu, Andrei, Vu, Van
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Eigenvalues of Euclidean random matrices [PDF]
Random Structures & Algorithms, 2008 AbstractWe study the spectral measure of large Euclidean random matrices. The entries of these matrices are determined by the relative position of n random points in a compact set Ωn of ℝd. Under various assumptions, we establish the almost sure convergence of the limiting spectral measure as the number of points goes to infinity.
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Randomized Algorithms for Matrices and Data [PDF]
Foundations and Trends® in Machine Learning, 2011 Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, largely since matrices are popular structures with which to model data drawn from a wide range of application domains, and this work was performed by individuals from ...
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On the Maximum Probability of Full Rank of Random Matrices over Finite Fields
MathematicsThe problem of determining the conditions under which a random rectangular matrix is of full rank is a fundamental question in random matrix theory, with significant implications for coding theory, cryptography, and combinatorics. In this paper, we study
Marija Delić, Jelena Ivetić
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IEEE Access, 2019 This paper addresses the asymptotic behavior of a particular type of information-plus-noise-type matrices, where the column and row numbers of the matrices are large and of the same order, while signals have diverged and the time delays of the channel ...
Guanping Lu +3 more
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