References analysis of the Wikipedia article "Random matrix" in the English version

arxiv.org

Russell, Nicholas; Chakhmakhchyan, Levon; O'Brien, Jeremy; Laing, Anthony (2017). "Direct dialling of Haar random unitary matrices". New J. Phys. 19 (3): 033007. arXiv:1506.06220. Bibcode:2017NJPh...19c3007R. doi:10.1088/1367-2630/aa60ed. S2CID 46915633.

Verbaarschot JJ, Wettig T (2000). "Random Matrix Theory and Chiral Symmetry in QCD". Annu. Rev. Nucl. Part. Sci. 50: 343–410. arXiv:hep-ph/0003017. Bibcode:2000ARNPS..50..343V. doi:10.1146/annurev.nucl.50.1.343. S2CID 119470008.

Franchini F, Kravtsov VE (October 2009). "Horizon in random matrix theory, the Hawking radiation, and flow of cold atoms". Phys. Rev. Lett. 103 (16): 166401. arXiv:0905.3533. Bibcode:2009PhRvL.103p6401F. doi:10.1103/PhysRevLett.103.166401. PMID 19905710. S2CID 11122957.

Sánchez D, Büttiker M (September 2004). "Magnetic-field asymmetry of nonlinear mesoscopic transport". Phys. Rev. Lett. 93 (10): 106802. arXiv:cond-mat/0404387. Bibcode:2004PhRvL..93j6802S. doi:10.1103/PhysRevLett.93.106802. PMID 15447435. S2CID 11686506.

Rychkov VS, Borlenghi S, Jaffres H, Fert A, Waintal X (August 2009). "Spin torque and waviness in magnetic multilayers: a bridge between Valet-Fert theory and quantum approaches". Phys. Rev. Lett. 103 (6): 066602. arXiv:0902.4360. Bibcode:2009PhRvL.103f6602R. doi:10.1103/PhysRevLett.103.066602. PMID 19792592. S2CID 209013.

Janssen M, Pracz K (June 2000). "Correlated random band matrices: localization-delocalization transitions". Phys. Rev. E. 61 (6 Pt A): 6278–86. arXiv:cond-mat/9911467. Bibcode:2000PhRvE..61.6278J. doi:10.1103/PhysRevE.61.6278. PMID 11088301. S2CID 34140447.

Zumbühl DM, Miller JB, Marcus CM, Campman K, Gossard AC (December 2002). "Spin-orbit coupling, antilocalization, and parallel magnetic fields in quantum dots". Phys. Rev. Lett. 89 (27): 276803. arXiv:cond-mat/0208436. Bibcode:2002PhRvL..89A6803Z. doi:10.1103/PhysRevLett.89.276803. PMID 12513231. S2CID 9344722.

Bahcall SR (December 1996). "Random Matrix Model for Superconductors in a Magnetic Field". Phys. Rev. Lett. 77 (26): 5276–5279. arXiv:cond-mat/9611136. Bibcode:1996PhRvL..77.5276B. doi:10.1103/PhysRevLett.77.5276. PMID 10062760. S2CID 206326136.

Tropp, J. (2011). "User-Friendly Tail Bounds for Sums of Random Matrices". Foundations of Computational Mathematics. 12 (4): 389–434. arXiv:1004.4389. doi:10.1007/s10208-011-9099-z. S2CID 17735965.

Yang, Greg (2022). "Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer". arXiv:2203.03466v2 [cs.LG].

Wainrib, Gilles; Touboul, Jonathan (March 2013). "Topological and Dynamical Complexity of Random Neural Networks". Physical Review Letters. 110 (11): 118101. arXiv:1210.5082. Bibcode:2013PhRvL.110k8101W. doi:10.1103/PhysRevLett.110.118101. PMID 25166580. S2CID 1188555.

Timme, Marc; Wolf, Fred; Geisel, Theo (February 2004). "Topological Speed Limits to Network Synchronization". Physical Review Letters. 92 (7): 074101. arXiv:cond-mat/0306512. Bibcode:2004PhRvL..92g4101T. doi:10.1103/PhysRevLett.92.074101. PMID 14995853. S2CID 5765956.

Burda, Z; Kornelsen, J; Nowak, MA; Porebski, B; Sboto-Frankenstein, U; Tomanek, B; Tyburczyk, J (2013). "Collective Correlations of Brodmann Areas fMRI Study with RMT-Denoising". Acta Physica Polonica B. 44 (6): 1243. arXiv:1306.3825. Bibcode:2013AcPPB..44.1243B. doi:10.5506/APhysPolB.44.1243.

Chiani M (2014). "Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution". Journal of Multivariate Analysis. 129: 69–81. arXiv:1209.3394. doi:10.1016/j.jmva.2014.04.002. S2CID 15889291.

Meckes, Elizabeth (2021-01-08). "The Eigenvalues of Random Matrices". arXiv:2101.02928 [math.PR].

Erdős, László; Schlein, Benjamin; Yau, Horng-Tzer (April 2009). "Local Semicircle Law and Complete Delocalization for Wigner Random Matrices". Communications in Mathematical Physics. 287 (2): 641–655. arXiv:0803.0542. Bibcode:2009CMaPh.287..641E. doi:10.1007/s00220-008-0636-9. ISSN 0010-3616.

Bourgade, Paul; Yau, Horng-Tzer; Yin, Jun (2014-08-01). "Local circular law for random matrices". Probability Theory and Related Fields. 159 (3): 545–595. arXiv:1206.1449. doi:10.1007/s00440-013-0514-z. ISSN 1432-2064.

Erdős, L.; Péché, S.; Ramírez, J.A.; Schlein, B.; Yau, H.T. (2010). "Bulk universality for Wigner matrices". Communications on Pure and Applied Mathematics. 63 (7): 895–925. arXiv:0905.4176. doi:10.1002/cpa.20317.

Tao, Terence; Vu, Van H. (2010). "Random matrices: universality of local eigenvalue statistics up to the edge". Communications in Mathematical Physics. 298 (2): 549–572. arXiv:0908.1982. Bibcode:2010CMaPh.298..549T. doi:10.1007/s00220-010-1044-5. S2CID 16594369.

doi.org

Wigner, Eugene P. (1955). "Characteristic Vectors of Bordered Matrices With Infinite Dimensions". Annals of Mathematics. 62 (3): 548–564. doi:10.2307/1970079. ISSN 0003-486X. JSTOR 1970079.

Block, R. C.; Good, W. M.; Harvey, J. A.; Schmitt, H. W.; Trammell, G. T., eds. (1957-07-01). Conference on Neutron Physics by Time-Of-Flight Held at Gatlinburg, Tennessee, November 1 and 2, 1956 (Report ORNL-2309). Oak Ridge, Tennessee: Oak Ridge National Lab. doi:10.2172/4319287. OSTI 4319287.

Bohigas, O.; Giannoni, M.J.; Schmit, Schmit (1984). "Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws". Phys. Rev. Lett. 52 (1): 1–4. Bibcode:1984PhRvL..52....1B. doi:10.1103/PhysRevLett.52.1.

Aaronson, Scott; Arkhipov, Alex (2013). "The computational complexity of linear optics". Theory of Computing. 9: 143–252. doi:10.4086/toc.2013.v009a004.

Callaway DJE (April 1991). "Random matrices, fractional statistics, and the quantum Hall effect". Phys. Rev. B. 43 (10): 8641–8643. Bibcode:1991PhRvB..43.8641C. doi:10.1103/PhysRevB.43.8641. PMID 9996505.

Wishart 1928 Wishart, J. (1928). "Generalized product moment distribution in samples". Biometrika. 20A (1–2): 32–52. doi:10.1093/biomet/20a.1-2.32.

von Neumann & Goldstine 1947 von Neumann, J.; Goldstine, H.H. (1947). "Numerical inverting of matrices of high order". Bull. Amer. Math. Soc. 53 (11): 1021–1099. doi:10.1090/S0002-9904-1947-08909-6.

Edelman & Rao 2005 Edelman, A.; Rao, N.R (2005). "Random matrix theory". Acta Numerica. 14: 233–297. Bibcode:2005AcNum..14..233E. doi:10.1017/S0962492904000236. S2CID 16038147.

Keating, Jon (1993). "The Riemann zeta-function and quantum chaology". Proc. Internat. School of Phys. Enrico Fermi. CXIX: 145–185. doi:10.1016/b978-0-444-81588-0.50008-0. ISBN 9780444815880.

Sompolinsky, H.; Crisanti, A.; Sommers, H. (July 1988). "Chaos in Random Neural Networks". Physical Review Letters. 61 (3): 259–262. Bibcode:1988PhRvL..61..259S. doi:10.1103/PhysRevLett.61.259. PMID 10039285. S2CID 16967637.

Rajan, Kanaka; Abbott, L. (November 2006). "Eigenvalue Spectra of Random Matrices for Neural Networks". Physical Review Letters. 97 (18): 188104. Bibcode:2006PhRvL..97r8104R. doi:10.1103/PhysRevLett.97.188104. PMID 17155583.

Muir, Dylan; Mrsic-Flogel, Thomas (2015). "Eigenspectrum bounds for semirandom matrices with modular and spatial structure for neural networks" (PDF). Phys. Rev. E. 91 (4): 042808. Bibcode:2015PhRvE..91d2808M. doi:10.1103/PhysRevE.91.042808. PMID 25974548.

Vergani, Alberto A.; Martinelli, Samuele; Binaghi, Elisabetta (July 2019). "Resting state fMRI analysis using unsupervised learning algorithms". Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization. 8 (3). Taylor&Francis: 2168–1171. doi:10.1080/21681163.2019.1636413.

Soize, C. (2005-04-08). "Random matrix theory for modeling uncertainties in computational mechanics" (PDF). Computer Methods in Applied Mechanics and Engineering. 194 (12–16): 1333–1366. Bibcode:2005CMAME.194.1333S. doi:10.1016/j.cma.2004.06.038. ISSN 1879-2138. S2CID 58929758.

Bohigas, Oriol; Weidenmuller, Hans (2015). Akemann, Gernot; Baik, Jinho; Di Francesco, Philippe (eds.). "History – an overview". academic.oup.com. pp. 15–40. doi:10.1093/oxfordhb/9780198744191.013.2. ISBN 978-0-19-874419-1. Retrieved 2024-04-22.

Livan, Giacomo; Novaes, Marcel; Vivo, Pierpaolo (2018), Livan, Giacomo; Novaes, Marcel; Vivo, Pierpaolo (eds.), "Classified Material", Introduction to Random Matrices: Theory and Practice, SpringerBriefs in Mathematical Physics, vol. 26, Cham: Springer International Publishing, pp. 15–21, doi:10.1007/978-3-319-70885-0_3, ISBN 978-3-319-70885-0, retrieved 2023-05-17

.Marčenko, V A; Pastur, L A (1967). "Distribution of eigenvalues for some sets of random matrices". Mathematics of the USSR-Sbornik. 1 (4): 457–483. Bibcode:1967SbMat...1..457M. doi:10.1070/SM1967v001n04ABEH001994.

Pastur 1973 Pastur, L.A. (1973). "Spectra of random self-adjoint operators". Russ. Math. Surv. 28 (1): 1–67. Bibcode:1973RuMaS..28....1P. doi:10.1070/RM1973v028n01ABEH001396. S2CID 250796916.

Pastur, L.; Shcherbina, M. (1995). "On the Statistical Mechanics Approach in the Random Matrix Theory: Integrated Density of States". J. Stat. Phys. 79 (3–4): 585–611. Bibcode:1995JSP....79..585D. doi:10.1007/BF02184872. S2CID 120731790.

Johansson, K. (1998). "On fluctuations of eigenvalues of random Hermitian matrices". Duke Math. J. 91 (1): 151–204. doi:10.1215/S0012-7094-98-09108-6.

Pastur, L.A. (2005). "A simple approach to the global regime of Gaussian ensembles of random matrices". Ukrainian Math. J. 57 (6): 936–966. doi:10.1007/s11253-005-0241-4. S2CID 121531907.

Pastur, L.; Shcherbina, M. (1997). "Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles". Journal of Statistical Physics. 86 (1–2): 109–147. Bibcode:1997JSP....86..109P. doi:10.1007/BF02180200. S2CID 15117770.

Deift, P.; Kriecherbauer, T.; McLaughlin, K.T.-R.; Venakides, S.; Zhou, X. (1997). "Asymptotics for polynomials orthogonal with respect to varying exponential weights". International Mathematics Research Notices. 1997 (16): 759–782. doi:10.1155/S1073792897000500.

Rider, B (2003-03-28). "A limit theorem at the edge of a non-Hermitian random matrix ensemble". Journal of Physics A: Mathematical and General. 36 (12): 3401–3409. Bibcode:2003JPhA...36.3401R. doi:10.1088/0305-4470/36/12/331. ISSN 0305-4470.

harvard.edu

ui.adsabs.harvard.edu

Edelman & Rao 2005 Edelman, A.; Rao, N.R (2005). "Random matrix theory". Acta Numerica. 14: 233–297. Bibcode:2005AcNum..14..233E. doi:10.1017/S0962492904000236. S2CID 16038147.

Pastur 1973 Pastur, L.A. (1973). "Spectra of random self-adjoint operators". Russ. Math. Surv. 28 (1): 1–67. Bibcode:1973RuMaS..28....1P. doi:10.1070/RM1973v028n01ABEH001396. S2CID 250796916.

jstor.org

Wigner, Eugene P. (1955). "Characteristic Vectors of Bordered Matrices With Infinite Dimensions". Annals of Mathematics. 62 (3): 548–564. doi:10.2307/1970079. ISSN 0003-486X. JSTOR 1970079.

Turnovsky, Stephen (1974). "The stability properties of optimal economic policies". American Economic Review. 64 (1): 136–148. JSTOR 1814888.

nih.gov

pubmed.ncbi.nlm.nih.gov

semanticscholar.org

api.semanticscholar.org

Pennington, Jeffrey; Bahri, Yasaman (2017). "Geometry of Neural Network Loss Surfaces via Random Matrix Theory". ICML'17: Proceedings of the 34th International Conference on Machine Learning. 70. S2CID 39515197.

Edelman & Rao 2005 Edelman, A.; Rao, N.R (2005). "Random matrix theory". Acta Numerica. 14: 233–297. Bibcode:2005AcNum..14..233E. doi:10.1017/S0962492904000236. S2CID 16038147.

Pastur 1973 Pastur, L.A. (1973). "Spectra of random self-adjoint operators". Russ. Math. Surv. 28 (1): 1–67. Bibcode:1973RuMaS..28....1P. doi:10.1070/RM1973v028n01ABEH001396. S2CID 250796916.

Pastur, L.A. (2005). "A simple approach to the global regime of Gaussian ensembles of random matrices". Ukrainian Math. J. 57 (6): 936–966. doi:10.1007/s11253-005-0241-4. S2CID 121531907.

tandfonline.com

Random matrix (English Wikipedia)

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