Wilson loops and random matrices
Sign Up to like & getrecommendations! Published in 2024 at "Journal of High Energy Physics"
DOI: 10.1007/jhep07(2024)203
Abstract: Linear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices. This mechanism does not depend on the… read more here.
Keywords: wilson loops; random matrices; loops random;
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
Concentration and moment inequalities for sums of independent heavy-tailed random matrices
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DOI: 10.1007/s00440-025-01412-6
Abstract: We prove Fuk-Nagaev and Rosenthal-type inequalities for sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only low orders. Our bounds depend on the “intrinsic”… read more here.
Keywords: moment inequalities; random matrices; heavy tailed; sums independent ... See more keywords
Average Discrete Energies of Spectra of Gaussian Random Matrices
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Sciences"
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
Identifying patterns using cross-correlation random matrices derived from deterministic and stochastic differential equations.
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DOI: 10.1063/5.0233321
Abstract: Cross-correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C… read more here.
Keywords: correlation random; random matrices; deterministic stochastic; cross correlation ... See more keywords