Spectral analysis of stochastic recurrence systems of growing dimension under G-condition. Canonical equation K 91

Random Operators and Stochastic Equations

Volumn 17, Issue 3, 2009, Pages 243-274

  Girko, V L ^a   Vladimirova, A I ^b  

^a INSTITUTE OF MATHEMATICS   (Ukraine)

^b Kiev Technical University   (Ukraine)

Author keywords

Canonical equations; Eigenvalues; Random matrix

Indexed keywords

EID: 83255168993     PISSN: 09266364     EISSN: 1569397X     Source Type: Journal    
DOI: 10.1515/ROSE.2009.017     Document Type: Article

References (46)

1. P. Bougerol and J. Lacroix, Products of Random Matrices with Applications to Schrödinger Operators, Birkhäuser, Boston-Basel-Stuttgart, 1985.
2. J. Bretagnolle and D. Dacunha-Castelle, Théorèmes limites à distance finie pour les marches aléatoires, Ann. Inst. Henri Poincaré, Nouv. Sé r., Sect. B 4 (1968), pp. 25-73.
3. G. P. Butsan, Stokhasticheskie polugruppi (Stochastic semigroups), Naukova Dumka, Kiev, 1977 (Russian).
4. A. S. Chani, Asymptotic behavior of the products of random matrices with values on a solvable Lie algebra, Ukrainian Mathematical Journal 45(7) (1993), pp. 1045-1048.
5. A. Crisanti, G. Paladin, M. Serva and A. Vulpiani, Products of random matrices for disordered systems, Phys. Rev. E 49 (1994), pp. R953-R955.
6. A. Crisanti G. Paladin and A. Vulpiani, Products of Random Matrices in Statistical Physics, Springer-Verlag, Berlin, 1993.
7. F. J. Dyson, The dynamics of disordered linear chain, Phys. Rev. 92(6) (1953), pp. 1331-1338.
8. F. J. Dyson, A Brownian-motion model for the eigenvalue of a random matrix, J. Math. Phys. 3(6) (1962), pp. 31-60.
9. F. J. Dyson, Correlations between eigenvalues of a random matrix, Commun. Math. Phys. 19 (1970), pp. 235-250.
10. H. Furstenberg and J. Kifer, Random matrix products and measures on projective spaces, Isr. J. Math. 46 (1983), pp. 12-32.
11. H. Furstenberg and H. Kesten, Products of random matrices, Ann. Math. Statist. 2 (1960), pp. 457-469.
12. J. Ginibre, Statistical ensembles of complex, quaternion, and real matrices, J. Math. Phys. 6 (1965), pp. 440-449.
13. V. L. Girko, A limit theorem for products of random matrices, Theory Probab. Appl. 21(1) (1976), pp. 197-199.
14. V. L. Girko, Spectral theory of random matrices, Theory Probab. Appl. 21(1) (1976), pp. 209-211.
15. V. L. Girko, Limit theorems for the eigenvalues of products of independent random matrices with nonnegative entries, Calculating and Applied Mathematics 42 (1980), pp. 29-35 (Russian).
16. V. L. Girko, On a new method for proving some limit theorems for products of independent random matrices, Theory Probab. Math. Stat. 22 (1981), pp. 35-47.
17. V. L. Girko, Central limit theorem for functional of products of certain random matrices, Theory Probab. Appl. 26(4) (1981), pp. 865-866.
18. V. L. Girko, Central limit theorem for functional of product of independent random matrices, Calculating and Applied Mathematics 47 (1982), pp. 118-122 (Russian).
19. V. L. Girko, Limit theorems for product of independent random matrices with positive entries, Theory Probab. Appl., 27(4) (1982), pp. 837-844.
20. V. L. Girko and G. V. Akulov, The theorems of the law of large number type for functionals of product of random matrices, Theory of Random Processes 15 (1987), pp. 16-19 (Russian).
21. 40, Simulation and Optimization of Complex Systems, Bulletin of Kiev University 7 (1988), pp. 10-13 (Russian).
22. V. L. Girko, An Introduction to Statistical Analysis of Random Arrays, Publishing VSP, 1998.
23. V. L. Girko, Theory of Stochastic Canonical Equations, Vol. I, Publishing Kluwer, 2001.
24. V. L. Girko, Theory of Stochastic Canonical Equations, Vol. II, Publishing Kluwer, 2001.
25. I. Goldsheid and Y. Guivarc'h, Dimension de la loi gaussienne pour un produit de matrices aléatoires indépendantes et adhérence de Zariski, C. R. Acad. Sci. Paris Ser. I Math. 313 (1991), pp. 305-308.
26. I. Goldsheid, Lyapunov exponents and asymptotic behaviour of the product of random matrices, Lect. Notes Math. 1486, pp. 23-37, 1991.
27. E. Gudowska-Nowak, R. A. Janik, J. Jurkiewicz and M. A. Nowak, Infinite products of large random matrices and matrix-valued diffusion, Nucl. Phys. B 670 (2003), pp. 479-507. (Pubitemid 37223523)
28. E. Gudowska-Nowak, R. A. Janik, J. Jurkiewicz and M. A. Nowak, Diffusion process of large random matrices, Acta Phys. Pol. B 34 (2003), pp. 4835-4853.
29. Y. Guivarc'h, Quelques propriétés asymptotiques des produits de matrices aléatoires, Lect. Notes Math. 774, pp. 176-250, 1980.
30. Y. Guivarc'h, Sur les exposants de Liapunoff des marches aléatoires à pas markovien, C. R. Acad. Sci. Paris Ser. I Math. 292 (1981), pp. 327-329.
31. Y. Guivarc'h and A. Raugi, Products of random matrices: convergence theorems. Contemp. Math. 50 (1986), pp. 31-54.
32. Y. Guivarc'h and A. Raugi, Propriétés de contraction d'un semi-groupe de matrices inversibles. Coefficients de Liapunoff d'un produit de matrices aléatoires indépendantes, Isr. J. Math. 65 (1989), pp. 165-196.
33. Y. Guivarc'h, Produits de matrices aléatoires et application aux propriétés géométriques des sous-groupes du groupe linéaire, Ergodic Theory Dyn. Syst. 10 (1990), pp. 483-512.
34. H. Kesten, Random difference equations and renewal theory for products of random matrices, Acta Math., 131 (1973), pp. 208-248.
35. V. I. Oseledets, A multiplicative ergodic theorem. Characteristic Lyapunov exponents of dynamical systems, Trudy Moskov. Mat. Obshch. 19 (1968), pp. 179-210;
36. English transl. Trans. Mosc. Math. Soc. 19 (1968), pp. 197-231.
37. C. E. Porter. Statistical Theories of Spectra: Fluctuations, Collection of Reprints and Original Papers, Academic Press, New York, 1965.
38. V. N. Tutubalin, On limit theorems for products of random matrices, Teor. Veroyatnost. i Primenen. 10 (1965), pp. 19-32;
39. English transl. Theory Probab. Appl. 10 (1965).
40. A. I. Vladimirova, Self averaging of normalized spectral functions of some product of independent random matrices of growing dimension, Random Oper. Stoch. Equ. 15(3) (2007), pp. 253-270.
41. A. I. Vladimirova, Limit theorems for solutions of recursion equations with random parameters, Vychisl. Prikl. Mat. 47 (1982), pp. 126-130 (Russian).
42. A. I. Vladimirova, Asymptotic distributions of the estimators of the parameters of the control systems, The Thesis of Third Republic Conference "Calculation Mathematics in the Contemporary Science-Technical Progress", Kiev, 1982 (Russian).
43. A. I. Vladimirova, Asymptotic normality of estimates of parameters of discrete control systems and the perturbation method in minimax estimation problems, Vychisl. Prikl. Mat. 49 (1983), pp. 121-126 (Russian).
44. A. I. Vladimirova, Estimation of solutions of systems of equations with multiplicative noise in a system of observations, Issled. Operatsii i ASU 21 (1983), pp. 30-32 (Russian).
45. R. Wegmann, The asymptotic eigenvalue-distribution for a certain class of random matrices, J. Math. Anal. Appl. 56 (1976), pp. 113-132.
46. E. P. Wigner, Random matrices in physics, SIAM Rev. 9(1) (1967), pp. 1-23.