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@article{AA_2011_23_1_a5, author = {L. A. Pastur}, title = {On the links between random operator and random matrix theories}, journal = {Algebra i analiz}, pages = {169--199}, publisher = {mathdoc}, volume = {23}, number = {1}, year = {2011}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2011_23_1_a5/} }
L. A. Pastur. On the links between random operator and random matrix theories. Algebra i analiz, Tome 23 (2011) no. 1, pp. 169-199. http://geodesic.mathdoc.fr/item/AA_2011_23_1_a5/
[1] Aizenman M., Germinet F., Klein A., Warzel S., “On Bernoulli decompositions for random variables, concentration bounds, and spectral localization”, Probab. Theory Related Fields, 143 (2009), 219–238 | DOI | MR | Zbl
[2] Akhiezer N. I., Glazman I. M., Teoriya lineinykh operatorov v gilbertovom prostranstve, v. 1, 2, 3-e izd., Vischa shk., Kharkov, 1977–1978
[3] Anderson G. W., Guionnet A., Zeitouni O., An introduction to random matrices, Cambridge Univ. Press, Cambridge, 2009 | MR | Zbl
[4] Bachmann S., De Roeck W., From the Anderson model on a strip to the DMPK equation and random matrix theory, arXiv: 0912.1574
[5] Bai Z., Silverstein J. W., Spectral analysis of large dimensional random matrices, Springer, New York, 2010 | MR
[6] Ben Arous G., Péché S., “Universality of local eigenvalue statistics for some sample covariance matrices”, Comm. Pure Appl. Math., 58 (2005), 1316–1357 | DOI | MR | Zbl
[7] Berezanskii Yu. M., Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Nauk. dumka, Kiev, 1965 | MR
[8] Bogachev V., Gaussovskie mery, Nauka, M., 1997 | MR | Zbl
[9] Brézin E., Hikami S., “Correlations of nearby levels induced by a random potential”, Nuclear Phys. B, 479 (1996), 697–706 | DOI | MR | Zbl
[10] Combes J.-M., Germinet F., Klein A., “Generalized eigenvalue-counting estimates for the Anderson model”, J. Stat. Phys., 135 (2009), 201–216 | DOI | MR | Zbl
[11] Disertori M., Pinson H., Spencer T., “Density of states for random band matrices”, Comm. Math. Phys., 232 (2002), 83–124 | DOI | MR | Zbl
[12] Disertori M., Kirsch W., Klein A., Klopp F., Rivasseau V., Random Schrödinger operators, Panoramas et Synthèses [Panoramas and Syntheses], 25, Soc. Math. France, Paris, 2008 | MR | Zbl
[13] Efetov K., Supersymmetry in disorder and chaos, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl
[14] Erdös L., Universality of Wigner random matrices: a survey of recent results, arXiv: 1004.0861
[15] Erdös L., Knowles A., Quantum diffusion and eigenfunction delocalization in a random band matrix model, arXiv: 1002.1695
[16] Forrester P., Log-gas and random matrices http://www.ms.unimelb.edu.au/~matpjf/matpjf.html
[17] Fyodorov Y. V., Mirlin A. D., “Scaling properties of localization in random band matrices: a $\sigma$-model approach”, Phys. Rev. Lett., 67 (1991), 2405–2409 | DOI | MR | Zbl
[18] Hemmer P. C., Lebowitz J. L., “Systems with weak long-range potentials”, Phase Transitions and Critical Phenomena, v. 5b, eds. C. Domb, M. S. Green, Acad. Press, London, 1976, 107–203 | MR
[19] Johansson K., “Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices”, Comm. Math. Phys., 215 (2001), 683–705 | DOI | MR | Zbl
[20] Johansson K., Universality for certain Hermitian Wigner matrices under weak moment conditions, arXiv: 0910/4467
[21] Khorunzhy A., Khoruzhenko B., Pastur L., Shcherbina M., “Large-n limit in statistical mechanics and the spectral theory of disordered systems”, Phase Transitions and Critical Phenomena, 15, eds. C. Domb, J. Lebowitz, Acad. Press, New York, 1992, 74–239
[22] Khorunzhy A., Pastur L., “Limits of infinite interaction radius, dimensionality and the number of components for random operators with off-diagonal randomness”, Comm. Math. Phys., 153 (1993), 605–646 | DOI | MR | Zbl
[23] Kirsch W., Lenoble O., Pastur L., “On the Mott formula for the ac conductivity and binary correlators in the strong localization regime of disordered systems”, J. Phys. A, 36 (2003), 12157–12180 | DOI | MR | Zbl
[24] Lifshits I. M., Gredeskul S. A., Pastur L. A., Vvedenie v teoriyu neuporyadochennykh sistem, Nauka, M., 1982 | MR
[25] Lytova A., Pastur L., “Central limit theorem for linear eigenvalue statistics of random matrices with independent entries”, Ann. Probab., 37 (2009), 1778–1840 | DOI | MR | Zbl
[26] Marchenko V. A., Pastur L. A., “Raspredelenie sobstvennykh znachenii v nekotorykh ansamblyakh sluchainykh matrits”, Mat. sb., 72(114):4 (1967), 507–536 | MR | Zbl
[27] Mehta M. L., Random matrices, Pure Appl. Math., 142, Elsevier, Amsterdam, 2004 | MR | Zbl
[28] Mirlin A., Fyodorov Ya., “The statistics of eigenvector components of random band matrices: analytical results”, J. Phys. A, 26 (1993), L551–L558 | DOI | MR
[29] Molchanov S. A., Pastur L. A., Khorunzhii A. M., “Raspredelenie sobstvennykh znachenii sluchainykh poloskovykh matrits v predele ikh beskonechnogo poryadka”, Teor. mat. fiz., 90:2 (1992), 163–178 | MR | Zbl
[30] Muirhead R. J., Aspects of multivariate statistical theory, Wiley, New York, 1982 | MR | Zbl
[31] Neu P., Speicher R., “Rigorous mean-field model for coherent-potential approximation: Anderson model with free random variables”, J. Stat. Phys., 80 (1995), 1279–1308 | DOI | MR | Zbl
[32] Pajor A., Pastur L., “On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution”, Studia Math., 195 (2009), 11–29 | DOI | MR | Zbl
[33] Pastur L. A., “O spektre sluchainykh matrits”, Teor. mat. fiz., 10:1 (1972), 102–112 | MR
[34] Pastur L., “A simple approach to the global regime of Gaussian ensembles of random matrices”, Ukr. mat. zh., 57:6 (2005), 790–817 | MR | Zbl
[35] Pastur L., “Eigenvalue distribution of random matrices”, Random Media 2000, Lectures from the Summer School “Random Media 2000” held in Mandralin, ed. J. Wehr, Poland. ICM Warsaw Univ., Warsaw, 2007, 95–206
[36] Pastur L., Figotin A., Spectra of random and almost-periodic operators, Grundlehren Math. Wiss., 297, Springer, Berlin, 1992 | MR | Zbl
[37] Pastur L., Shcherbina M., “Bulk universality and related properties of Hermitian matrix models”, J. Stat. Phys., 130 (2008), 205–250 | DOI | MR | Zbl
[38] Pastur L., Vasilchuk V., “On the law of addition of random matrices”, Comm. Math. Phys., 214 (2000), 249–286 | DOI | MR | Zbl
[39] Pastur L., Vasilchuk V., “On the law of addition of random matrices: covariance and the central limit theorem for traces of resolvent”, Probability and Mathematical Physics, CRM Proc. Lecture Notes, 42, Amer. Math. Soc., Providence, RI, 2007, 399–416 | MR | Zbl
[40] Rowlands D. A., “Short-range correlations in disordered systems: nonlocal coherent-potential approximation”, Rep. Prog. Phys., 72 (2009), 086501 | DOI
[41] Schenker J., “Eigenvector localization for random band matrices with power law band width”, Comm. Math. Phys., 290 (2009), 1065–1097 | DOI | MR | Zbl
[42] Shcherbina T., “On universality of bulk local regime of the deformed Gaussian unitary ensemble”, Zh. mat. fiz., anal., geom., 5:4 (2009), 396–433 | MR
[43] Spencer T., “Random banded and sparse matrices”, The Oxford Handbook of Random Matrix Theory, eds. G. Akemann, J. Baik, Ph. DiFrancesco, Oxford Univ. Press, Oxford, 2011
[44] Stanley H., Introduction to phase transitions and critical phenomena, Clarendon Press, Oxford, 1971
[45] Tao T., Vu V., “Random matrices: universality of local eigenvalue statistics”, Acta Math. (to appear) , arXiv: 0906/0510
[46] Tao T., Vu V., Random covariance matrices: universality of local statistics of eigenvalues, arXiv: 0912/0966
[47] Thompson C. J., Mathematical statistical mechanics, Princeton Univ. Press, Princeton, 1979 | MR | Zbl
[48] Virag B., Valko V., Random Schrödinger operators on long boxes, noise explosion and the GOE, arXiv: 0912/0097
[49] Voiculescu D., “Aspects of free probability”, XIVth International Congress on Mathematical Physics, World Sci. Publ., Hackensack, NJ, 2005, 145–157 | MR
[50] Wegner F., “Disordered electronic systems as a model of interacting matrices”, Phys. Rep., 67 (1980), 15–24 | DOI | MR