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Limiting eigenvalue distribution for band random matrices. (English. Russian original) Zbl 0794.15011

Theor. Math. Phys. 90, No. 2, 108-118 (1992); translation from Teor. Mat. Fiz. 90, No. 2, 163-178 (1992).
Summary: An equation is obtained for the Stieltjes transform of the normalized eigenvalue distribution of band random matrices in the limit in which the band width and rank of the matrix simultaneously tend to infinity. Conditions under which this limit agrees with the semicircle law are found.

MSC:

15B52 Random matrices (algebraic aspects)
15A18 Eigenvalues, singular values, and eigenvectors
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[1] T. Brody, J. Flores, J. French, P. A. Mello, A. Pandy, and S. S. Wong,Rev. Mod. Phys.,53, 385 (1981). · doi:10.1103/RevModPhys.53.385
[2] E. Brezin, C. Itzykson, and J. Zuber,J. Adv. Appl. Math.,1, 109 (1980). · Zbl 0453.05035 · doi:10.1016/0196-8858(80)90008-1
[3] Quantum Chaos and Statistical Nuclear Physics (eds. T. H. Seligman and H. Nishioka), Springer, Berlin (1986).
[4] L. A. Pastur,Usp. Mat. Nauk,28, 3 (1973).
[5] V. L. Gipko,Spectral Theory of Random Matrices [in Russian], Nauka, Moscow (1988).
[6] E. Wigner,Ann. Math.,62, 548 (1958). · Zbl 0067.08403 · doi:10.2307/1970079
[7] V. A. Marchenko and L. A. Pastur,Mat. Sb.,72, 507 (1967).
[8] I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur,Introduction to the Theory of Disordered Systems [in Russian], Nauka, Moscow (1982).
[9] G. Casati, L. Molinari, and F. Israilev,Phys. Rev. Lett.,64, 1851 (1990). · Zbl 1050.82500 · doi:10.1103/PhysRevLett.64.1851
[10] L. A. Pastur,Teor. Mat. Fiz.,10, 102 (1972).
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