Molchanov, S. A.; Pastur, L. A.; Khorunzhij, A. M. 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. Cited in 30 Documents MSC: 15B52 Random matrices (algebraic aspects) 15A18 Eigenvalues, singular values, and eigenvectors Keywords:Stieltjes transform; normalized eigenvalue distribution; band random matrices; semicircle law PDFBibTeX XMLCite \textit{S. A. Molchanov} et al., Theor. Math. Phys. 90, No. 2, 1 (1992; Zbl 0794.15011); translation from Teor. Mat. Fiz. 90, No. 2, 163--178 (1992) Full Text: DOI References: [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). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.