Domains of analytic continuation for the top Lyapunov exponent

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1. [B] G. Birkhoff, Extensions of Jentzch's Theorem, Trans. Am. Math Soc., Vol. 85, 1957, pp. 219-227. Zbl0079.13502MR87058
2. [BL] P. Bougerol and J. Lacroix, Products of Random Matrices with Applications to SchrödingerOperators, Birkhauser, Basel, 1985. Zbl0572.60001MR886674
3. [CKN1] J.E. Cohen, H. Kesten and C.M. Newman Eds., Random Matrices and Their Applications, Contemporary Math., Vol. 50, Am. Math. Soc., Providence, 1986. Zbl0581.00014MR841077
4. [CKN2] J.E. Cohen, H. Kesten and C.M. Newman, Oseledec's Multiplicative Ergodic Theorem: a Proof, in [CKN1]. Zbl0607.60026
5. [CN] J.E. Cohen and C.M. Newman, The Stability of Large Random Matrices and Their Products, Ann. Probab., Vol. 12, 1984, pp. 283-310. Zbl0543.60098MR735839
6. [F] H. Furnstenberg, Non-Commuting Random Products, Trans. Am. Math. Soc., Vol. 108, 1963, pp. 377-428. Zbl0203.19102MR163345
7. [FK] H. Furstenberg and H. Kesten, Products of Random Matrices, Ann. Math. Stat., Vol. 31, 1960, pp. 457-469. Zbl0137.35501MR121828
8. [GR] Y. Guivarch and A. Raugi, Frontière de Furstenberg, propriétés de contraction et théorèmes de convergence, Zeit. Wahr. verw. Gebeite, Vol. 69, 1985, pp. 187- 242. Zbl0558.60009MR779457
9. [GRo] R.C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall, 1965. Zbl0141.08601MR180696
10. [Hen] H. Hennion, Derivabilite du plus grand exposant caractéristique des produits de matrices aléatoires indépendantes à coefficients positifs, preprint, 1990. 
11. [Hop] E. Hopf, An Inequality for Positive Integral Linear Operators, J. Math. Mech., Vol. 12, 1963, pp. 683-692. Zbl0115.32501MR165325
12. [Ka] T. Kato, Perturbation Theory for Linear Operators, Second Edition, Springer-Verlag, 1976. Zbl0342.47009MR407617
13. [KP] R. Kenyon and Y. Peres, Intersecting Random Translates of Invariant Cantor Sets, Inventiones Math., Vol. 104, 1991, pp. 601-629. Zbl0745.28012MR1106751
14. [Key1] E.S. Key, Computable Examples of the Maximal Lyapunov Exponent, Probab. Th. Rel. Fields, Vol. 75, 1987, pp. 97-107. Zbl0595.60012MR879555
15. [Key2] E.S. Key, Lower Bounds for the Maximal Lyapunov Exponent, J. Theor. Probab., Vol. 3, 1990, pp. 447-487. Zbl0704.60011MR1057526
16. [LP1] E. Le Page, Théorèmes limites pour les produits de matrices aléatoires, in Probability Measures on Groups, H. HEYER Ed., Lect. Notes Math., No. 928, Springer-Verlag, 1982, pp. 258-303. Zbl0506.60019MR669072
17. [LP2] E. le PageRégularité du plus grand exposant caractéristique des produits de matrices aléatoires indépendantes et applications, Ann. Inst. Henri Poincaré, Vol. 25, 1989, pp. 109-142. Zbl0679.60010MR1001021
18. [Let] G. Letac, A Contraction Principle for Certain Markov Chains and Its Applications, in [CKN1]. Zbl0587.60057
19. [P] Y. Peres, Analytic dependence of Lyapunov exponents on transition probabilities, Proceedings of the 1990 Oberwolfach conference on Lyapunov exponents, L. ARNOLD et al. Ed., (to appear) Springer VerlagLect. Notes Math., No. 1486. Zbl0762.60005MR1178947
20. [R] D. Ruelle, Analyticity Properties of the Characteristic Exponents of Random Matrix Products, Adv. Math., Vol. 32, 1979, pp. 68-80. Zbl0426.58018MR534172
21. [S] E. Seneta, Non-Negative Matrices and Markov Chains, 2nd ed., Springer Verlag, 1981. Zbl0471.60001
22. [Wil] J.H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford University Press, 1965. Zbl0258.65037MR184422
23. [Wojt] M. Wojtkowski, On Uniform Contraction Generated by Positive Matrices, in [CKN1]. Zbl0584.60017

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