Random walks in random medium on ℤ and Lyapunov spectrum

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 40, Issue 3, 2004, Pages 309-336

  Brémont, Julien ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Cone; Lyapunov exponent; Markov chain; Random walk in random environment

Indexed keywords

EID: 2342659728     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpb.2003.10.006     Document Type: Article

References (17)

1. Alili S. Asymptotic behaviour for random walks in random environments J. Appl. Probab. 36 2 1999 334-349
2. Berman A. Plemmons R.J. Nonnegative Matrices in the Mathematical Sciences Classics in Applied Mathematics vol. 9 1994 Society for Industrial and Applied Mathematics (SIAM) Philadelphia, PA Revised reprint of the 1979 original
3. Bernasconi J. Schneider T. (Eds.), Physics in One Dimension 1981 Springer-Verlag Berlin
4. Bolthausen E. Goldsheid I. Recurrence and transience of random walks in random environments on a strip Com. Math. Phys. 214 2000 429-447
5. Brémont J. On the recurrence of random walks on ℤ in random medium C. R. Acad. Sci. Paris Sér. I Math. 333 11 2001 1011-1016
6. Brémont J. On some random walks on ℤ in random medium Ann. Probab. 30 3 2002 1266-1312
7. J. Brémont, Thèse de doctorat, Marches aléatoires en milieu aléatoire sur ℤ dynamique d'applications localement contractantes sur le Cercle, Université de Rennes I, 2002
8. Derriennic Y. Sur la récurrence des marches aléatoires unidimensionnelles en environnement aléatoire C. R. Acad. Sci. Paris Sér. I Math. 329 1 1999 65-70
9. Hennion H. Limit theorems for products of positive random matrices Ann. Probab. 25 4 1997 1545-1587
10. Key E.S. Recurrence and transience criteria for a random walk in a random environment Ann. Probab. 12 2 1984 529-560
11. Kozlov S.M. The averaging method and walks in inhomogeneous environments Uspekhi Mat. Nauk 40 2(242) 1985 61 120-238
12. Ledrappier F. Quelques propriétés des exposants caractéristiques Ecole d'été de Saint-Flour 1982 Lecture Notes in Math. vol. 1097 1984 305-396 Springer Berlin
13. Lëtchikov A.V. Localization of One-Dimensional Random Walks in Random Environments 1989 Harwood Academic Publishers Chur
14. Lëtchikov A.V. A criterion for the applicability of the central limit theorem to one-dimensional random walks in random environments Teor. Veroyatnost. i Primenen. 37 3 1992 576-580
15. Oseledec V.I. A multiplicative ergodic theorem. Characteristic Ljapunov exponents of dynamical systems Trudy Moskov. Mat. Obšč. 19 1968 179-210
16. Raugi A. Théorème ergodique multiplicatif. Produits de matrices aléatoires indépendantes Fascicule de probabilités 1997 43 Univ. Rennes I
17. Solomon F. Random walks in a random environment Ann. Probab. 3 1975 1-31