Erratum to: Black holes and random matrices
Sign Up to like & getrecommendations! Published in 2018 at "Journal of High Energy Physics"
DOI: 10.1007/jhep09(2018)002
Abstract: We have found a minor normalization error in some of the plots in this paper. This error has no effect on the qualitative or quantitative conclusions of the paper. read more here.
Keywords: holes random; erratum black; random matrices; black holes ... See more keywords
Propagation of Singular Behavior for Gaussian Perturbations of Random Matrices
Sign Up to like & getrecommendations! Published in 2018 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-018-3195-8
Abstract: We study the asymptotic behavior of the eigenvalues of Gaussian perturbations of large Hermitian random matrices for which the limiting eigenvalue density vanishes at a singular interior point or vanishes faster than a square root… read more here.
Keywords: gaussian perturbations; propagation singular; random matrices; singular behavior ... See more keywords
Products of Many Large Random Matrices and Gradients in Deep Neural Networks
Sign Up to like & getrecommendations! Published in 2018 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-019-03624-z
Abstract: We study products of random matrices in the regime where the number of terms and the size of the matrices simultaneously tend to infinity. Our main theorem is that the logarithm of the $$\ell _2$$… read more here.
Keywords: deep neural; many large; neural networks; products many ... See more keywords
Local spectral statistics of the addition of random matrices
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DOI: 10.1007/s00440-019-00932-2
Abstract: We consider the local statistics of $$H = V^* X V + U^* Y U$$H=V∗XV+U∗YU where V and U are independent Haar-distributed unitary matrices, and X and Y are deterministic real diagonal matrices. In the… read more here.
Keywords: local spectral; addition random; random matrices; statistics addition ... See more keywords
Edge universality for non-Hermitian random matrices
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DOI: 10.1007/s00440-020-01003-7
Abstract: We consider large non-Hermitian real or complex random matrices $$X$$ X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of… read more here.
Keywords: random matrices; non hermitian; non; edge universality ... See more keywords
Average Discrete Energies of Spectra of Gaussian Random Matrices
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DOI: 10.1007/s10958-019-4145-5
Abstract: We present exact formulas for the averages of various discrete energies of certain point processes in the plane and two-dimensional sphere. Specifically, we consider point processes defined by the spectra of gaussian random matrices and… read more here.
Keywords: random matrices; average discrete; discrete energies; spectra gaussian ... See more keywords
Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices
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DOI: 10.1016/j.aop.2021.168456
Abstract: Abstract Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the systems studied… read more here.
Keywords: theory; disordered mechanical; disordered crystals; mechanical systems ... See more keywords
RANDOM MATRICES WITH SLOW CORRELATION DECAY
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DOI: 10.1017/fms.2019.2
Abstract: 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… read more here.
Keywords: matrices slow; correlation; correlation decay; random matrices ... See more keywords
Immanants of blocks from random matrices in some unitary ensembles
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DOI: 10.1088/1751-8121/ac0984
Abstract: The permanent of unitary matrices and their blocks has attracted increasing attention in quantum physics and quantum computation because of connections with the Hong–Ou–Mandel effect and the boson sampling problem. In that context, it would… read more here.
Keywords: physics; unitary ensembles; random matrices; immanants blocks ... See more keywords
Characteristic Polynomials of Complex Random Matrices and Painlevé Transcendents
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DOI: 10.1093/imrn/rnaa111
Abstract: We study expectations of powers and correlation functions for characteristic polynomials of N×N non-Hermitian random matrices. For the 1-point and 2-point correlation function, we obtain several characterizations in terms of Painleve transcendents, both at finite-N… read more here.
Keywords: ginibre ensemble; characteristic polynomials; random matrices; polynomials complex ... See more keywords
On the Outlying Eigenvalues of a Polynomial in Large Independent Random Matrices
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DOI: 10.1093/imrn/rnz080
Abstract: Given a selfadjoint polynomial $P(X,Y)$ in two noncommuting selfadjoint indeterminates, we investigate the asymptotic eigenvalue behavior of the random matrix $P(A_N,B_N)$, where $A_N$ and $B_N$ are independent Hermitian random matrices and the distribution of $B_N$… read more here.
Keywords: random matrices; outlying eigenvalues; eigenvalues polynomial; almost surely ... See more keywords