Limit of infinite band width for product of two random matrices

Random Operators and Stochastic Equations

Volumn 5, Issue 4, 1997, Pages 325-336

  Khorunzhy, A ^a   Kirsch, W ^b  

^a B VERKIN INSTITUTE FOR LOW TEMPERATURE PHYSICS AND ENGINEERING   (Ukraine)

^b RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010050615     PISSN: 09266364     EISSN: 1569397X     Source Type: Journal    
DOI: 10.1515/rose.1997.5.4.325     Document Type: Article

References (21)

1. L. Bogachev, S. Molchanov and L. Pastur. On the level density of random band matrices, Mathem. Notes USSR 50, 1232-1242 (1991).
2. A. Bovier, V. Gayrard and P. Picco. Large deviations principles for the Hopfield model and Kac-Hopfield model, Prob. Theory Rei Fields 101, 511-546 (1995).
3. A. Boutet de Monvel, A. Khorunzhy and V. Vasilchuk. Limiting eigenvalue distribution of random matrices with correlated entries, Markov Processes and Related Fields 2, 607-636 (1996).
4. G. Casati, F. Izrailev and L. Molinari. Scaling properties of band random matrices, Phys. Rev. Lett. 64, 1851-1854 (1990).
5. B. Chirikov. The problem of quantum chaos. In: Chaos and Quantum Chaos Proceed. Blyderpoort, South Afrika (1992). Lect. Notes in Physics, vol. 411 Springer-Verlag, Berlin.
6. W. Donoghue. Monotone Matrix Functions and Analytic Continuation. Springer: Berlin, New York, 182p. (1974).
7. M. Feingold, D. M. Leitner and M. Wilkinson. Spectral statistics in semiclassical random-matrix ensembles. Phys. Rev. Lett. 66, 968-989 (1991).
8. Y. V. Fyodorov and A. D.Mirlin. Scaling properties of localization in random band matrices: a σ-model approach, Phys. Rev. Lett. 67, 2405-2409 (1991).
9. V. Girko, Spectral Theory of Random Matrices. Moscow, Nauka (1988).
10. V. Girko and W. Kirsch. Limit theorems for band random matrices whose entries have bounded variances. Random Oper. Stock. Eqs. 1, 181-191 (1993).
11. I. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sei. USA 79, 2554-2558 (1982).
12. A. Khorunzhy and L. Pastur. Limits of infinite dimensions, interaction radius and number of components for random operators with off-diagonal randomness, Commun. Math. Phys. 153, 605-646 (1993).
13. A. Khorunzhy and G. Rodgers. Eigenvalue distribution of large dilute random matrices. Accepted for publication in Math. Phys.
14. M. Kus, M. Lewenstein and F. Haake. Density of eigenvalues of random band matrices, Phys. Rev. A 44, 2800-2808 (1991).
15. V. Marchenko and L. Pastur, Eigenvalue distribution of certain ensembles of random matrices, Matematich. Sbornik, 72, 507-536 (1967).
16. S. Molchanov, L. Pastur, and A. Khorunzhy. Eigenvalue distribution of band random matrices in the limit of their infinite range, Theor. Math. Phys. 73, 1094 (1992).
17. L. Pastur and A. Figotin. Exactly soluble model of a spin glass, Sov. J. Low Temp. Phys. 3, 6, 378-383 (1977).
18. L. A. Pastur and A. L. Figotin. On the infinite range limit in theory of disordered systems, Teor. Matem. Fiz. 51, 380-388 (1982).
19. L. Pastur and A. Figotin. Spectra of Random and Almost Periodic Operators. Springer, Berlin (1992).
20. L. Pastur and A. Khorunzhy. On the eigenvalue distribution of the deformed Wigner ensemble of random matrices. In: V. Marchenko (ed.) Advances in Sov. Mathem., 19, AMS: Rhode Island, 97-127 (1994).
21. E. Wigner. Characteristic vectors of bordered matrices with infinite dimensions, Ann.Math. 62, 548-564 (1955).