Results 41 to 50 of about 182,487 (307)
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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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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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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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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THE SPECTRUM OF RANDOM INNER-PRODUCT KERNEL MATRICES
, 2013 We consider nxn matrices whose (i, j)th entry is f(X-i(T) X-j), where X-1,..., X-n are i.i.d. standard Gaussian in R-p, and f is a real-valued function. The weak limit of the eigenvalue distribution of these random matrices is studied at the limit when p,
Cheng, Xiuyuan, Singer, Amit
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Random matrices and holographic tensor models
Journal of High Energy Physics, 2017 We further explore the connection between holographic O(n) tensor models and random matrices. First, we consider the simplest non-trivial uncolored tensor model and show that the results for the density of states, level spacing and spectral form factor ...
Chethan Krishnan +2 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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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 WITH SLOW CORRELATION DECAY
Forum of Mathematics, Sigma, 2019 We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result
LÁSZLÓ ERDŐS +2 more
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