Results 31 to 40 of about 167,620 (262)
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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Incremental universality of Wigner random matrices [PDF]
Royal Society Open ScienceProperties of universality have essential relevance for the theory of random matrices usually called the Wigner ensemble. The issue was analysed up to recent years with detailed and relevant results.
Giovanni M. Cicuta, Mario Pernici
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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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Infinite Series of Singularities in the Correlated Random Matrices Product
Frontiers in Physics, 2021 We consider the product of a large number of two 2 × 2 matrices chosen randomly (with some correlation): at any round there are transition probabilities for the matrix type, depending on the choice at previous round. Previously, a functional equation has
Ruben Poghosyan, David B. Saakian
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Spectra of euclidean random matrices [PDF]
Nuclear Physics B, 1999 10 pages, 4 ...
Mézard, M., Parisi, G., Zee, A.
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Resilience of the rank of random matrices [PDF]
Combinatorics, Probability and Computing, 2020 AbstractLet M be an n × m matrix of independent Rademacher (±1) random variables. It is well known that if $n \leq m$, then M is of full rank with high probability. We show that this property is resilient to adversarial changes to M. More precisely, if $m \ge n + {n^{1 - \varepsilon /6}}$, then even after changing the sign of (1 – ε)m/2 entries, M is ...
Asaf Ferber, Kyle Luh, Gweneth McKinley
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The Smallest Singular Value Anomaly and the Condition Number Anomaly
Axioms, 2022 Let A be an arbitrary matrix in which the number of rows, m, is considerably larger than the number of columns, n. Let the submatrix Ai,i=1,…,m, be composed of the first i rows of A.
Achiya Dax
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RANDOM MATRICES: THE CIRCULAR LAW [PDF]
Communications in Contemporary Mathematics, 2008 Let x be a complex random variable with mean zero and bounded variance σ2. Let Nn be a random matrix of order n with entries being i.i.d. copies of x. Let λ1, …, λn be the eigenvalues of [Formula: see text]. Define the empirical spectral distributionμn of Nn by the formula [Formula: see text] The following well-known conjecture has been open since ...
Tao, Terence, Van, Vu
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