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Teoreticheskaya i Matematicheskaya Fizika, 1972, Volume 10, Number 1, Pages 102–112 (Mi tmf2643)  

This article is cited in 189 scientific papers (total in 189 papers)

On the spectrum of random matrices

L. A. Pastur
References:
Abstract: A study is made of the distribution of eigenvalues in a certain ensemble of random particles that contains as a special case the ensemble used by Wigner to give a statistical description of the energy levels of heavy nuclei, it is shown that the distribution function of the elgenvalues divided by the factor N (the order of the matrices) becomes nonrandom In the limit N and can be found by solving a definite functional equation.
Received: 11.01.1971
English version:
Theoretical and Mathematical Physics, 1972, Volume 10, Issue 1, Pages 67–74
DOI: https://doi.org/10.1007/BF01035768
Bibliographic databases:
Language: Russian
Citation: L. A. Pastur, “On the spectrum of random matrices”, TMF, 10:1 (1972), 102–112; Theoret. and Math. Phys., 10:1 (1972), 67–74
Citation in format AMSBIB
\Bibitem{Pas72}
\by L.~A.~Pastur
\paper On the spectrum of random matrices
\jour TMF
\yr 1972
\vol 10
\issue 1
\pages 102--112
\mathnet{http://mi.mathnet.ru/tmf2643}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=475502}
\transl
\jour Theoret. and Math. Phys.
\yr 1972
\vol 10
\issue 1
\pages 67--74
\crossref{https://doi.org/10.1007/BF01035768}
Linking options:
  • https://www.mathnet.ru/eng/tmf2643
  • https://www.mathnet.ru/eng/tmf/v10/i1/p102
  • This publication is cited in the following 189 articles:
    1. Hong Chang Ji, Jaewhi Park, “Tracy-Widom limit for free sum of random matrices”, Ann. Probab., 53:1 (2025)  crossref
    2. Vyacheslav L. Girko, “The global elliptic law, sand clock density and V-law. 40 years of the G-elliptic law”, Random Operators and Stochastic Equations, 2025  crossref
    3. Maxime Debertolis, Springer Theses, Quantum Impurity Problems in the Framework of Natural Orbitals, 2024, 95  crossref
    4. Wenping Cui, Jason W. Rocks, Pankaj Mehta, “An elementary mean-field approach to the spectral densities of random matrix ensembles”, Physica A: Statistical Mechanics and its Applications, 637 (2024), 129608  crossref
    5. Atsushi Yamamura, Hideo Mabuchi, Surya Ganguli, “Geometric Landscape Annealing as an Optimization Principle Underlying the Coherent Ising Machine”, Phys. Rev. X, 14:3 (2024)  crossref
    6. Jonathan Husson, Benjamin McKenna, “Large deviations for the largest eigenvalue of generalized sample covariance matrices”, Electron. J. Probab., 29:none (2024)  crossref
    7. Samuel Cure, Izaak Neri, “Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems”, SciPost Phys., 14:5 (2023)  crossref
    8. Wojciech Tarnowski, Dariusz Chruściński, Sergey Denisov, Karol Życzkowski, “Random Lindblad Operators Obeying Detailed Balance”, Open Syst. Inf. Dyn., 30:02 (2023)  crossref
    9. Ji Oon Lee, Yiting Li, “Spherical Sherrington–Kirkpatrick Model for Deformed Wigner Matrix with Fast Decaying Edges”, J Stat Phys, 190:2 (2023)  crossref
    10. Filipe C. Thewes, Matthias Krüger, Peter Sollich, “Composition Dependent Instabilities in Mixtures with Many Components”, Phys. Rev. Lett., 131:5 (2023)  crossref
    11. Peter J. Forrester, “A review of exact results for fluctuation formulas in random matrix theory”, Probab. Surveys, 20:none (2023)  crossref
    12. Huanchao Zhou, Zhidong Bai, Jiang Hu, “The Limiting Spectral Distribution of Large-Dimensional General Information-Plus-Noise-Type Matrices”, J Theor Probab, 36:2 (2023), 1203  crossref
    13. Stephan Gufler, Adrien Schertzer, Marius A. Schmidt, “On the concavity of the TAP free energy in the SK model”, Stochastic Processes and their Applications, 164 (2023), 160  crossref
    14. Leonid Pastur, Victor Slavin, “On random matrices arising in deep neural networks: General I.I.D. case”, Random Matrices: Theory Appl., 12:01 (2023)  crossref
    15. Dan Dai, Shuai-Xia Xu, Lun Zhang, “On the deformed Pearcey determinant”, Advances in Mathematics, 400 (2022), 108291  crossref
    16. Gökalp Alpan, Rostyslav Kozhan, “Hermitian and non-Hermitian perturbations of chiral Gaussian β-ensembles”, Journal of Mathematical Physics, 63:4 (2022)  crossref
    17. L. Pastur, “Eigenvalue distribution of large random matrices arising in deep neural networks: Orthogonal case”, Journal of Mathematical Physics, 63:6 (2022)  crossref
    18. Bertrand Lacroix-A-Chez-Toine, Yan V Fyodorov, “Counting equilibria in a random non-gradient dynamics with heterogeneous relaxation rates”, J. Phys. A: Math. Theor., 55:14 (2022), 144001  crossref
    19. Martinez-Finkelshtein A. Silva G.L.F., “Spectral Curves, Variational Problems and the Hermitian Matrix Model With External Source”, Commun. Math. Phys., 383:3 (2021), 2163–2242  crossref  isi
    20. Yiting Li, Kevin Schnelli, Yuanyuan Xu, “Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices”, Ann. Inst. H. Poincaré Probab. Statist., 57:1 (2021)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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