no. 3
Random walks in random medium on Z and Lyapunov spectrum
Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 3, pp. 309-336. 
@article{AIHPB_2004__40_3_309_0,
     author = {Br\'emont, Julien},
     title = {Random walks in random medium on {Z} and {Lyapunov} spectrum},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {309--336},
     publisher = {Elsevier},
     volume = {40},
     number = {3},
     year = {2004},
     doi = {10.1016/j.anihpb.2003.10.006},
     mrnumber = {2060456},
     zbl = {1042.60022},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2003.10.006/}
}
TY  - JOUR
AU  - Brémont, Julien
TI  - Random walks in random medium on Z and Lyapunov spectrum
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2004
SP  - 309
EP  - 336
VL  - 40
IS  - 3
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpb.2003.10.006/
DO  - 10.1016/j.anihpb.2003.10.006
LA  - en
ID  - AIHPB_2004__40_3_309_0
ER  - 
%0 Journal Article
%A Brémont, Julien
%T Random walks in random medium on Z and Lyapunov spectrum
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2004
%P 309-336
%V 40
%N 3
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpb.2003.10.006/
%R 10.1016/j.anihpb.2003.10.006
%G en
%F AIHPB_2004__40_3_309_0
Brémont, Julien. Random walks in random medium on Z and Lyapunov spectrum. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 3, pp. 309-336. doi : 10.1016/j.anihpb.2003.10.006. http://archive.numdam.org/articles/10.1016/j.anihpb.2003.10.006/

[1] S. Alili, Asymptotic behaviour for random walks in random environments, J. Appl. Probab. 36 (2) (1999) 334-349. | MR | Zbl

[2] A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Classics in Applied Mathematics, vol. 9, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1994, Revised reprint of the 1979 original. | MR | Zbl

[3] Physics in One Dimension, Springer-Verlag, Berlin, 1981. | MR

[4] E. Bolthausen, I. Goldsheid, Recurrence and transience of random walks in random environments on a strip, Com. Math. Phys. 214 (2000) 429-447. | MR | Zbl

[5] J. Brémont, On the recurrence of random walks on Z in random medium, C. R. Acad. Sci. Paris Sér. I Math. 333 (11) (2001) 1011-1016. | MR | Zbl

[6] J. Brémont, On some random walks on Z in random medium, Ann. Probab. 30 (3) (2002) 1266-1312. | MR | Zbl

[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] Y. Derriennic, Sur la récurrence des marches aléatoires unidimensionnelles en environnement aléatoire, C. R. Acad. Sci. Paris Sér. I Math. 329 (1) (1999) 65-70. | MR | Zbl

[9] H. Hennion, Limit theorems for products of positive random matrices, Ann. Probab. 25 (4) (1997) 1545-1587. | MR | Zbl

[10] E.S. Key, Recurrence and transience criteria for a random walk in a random environment, Ann. Probab. 12 (2) (1984) 529-560. | MR | Zbl

[11] S.M. Kozlov, The averaging method and walks in inhomogeneous environments, Uspekhi Mat. Nauk 40 (2(242)) (1985) 61-120, 238. | MR | Zbl

[12] F. Ledrappier, Quelques propriétés des exposants caractéristiques, in: Ecole d'été de Saint-Flour 1982, Lecture Notes in Math., vol. 1097, Springer, Berlin, 1984, pp. 305-396. | MR | Zbl

[13] A.V. Lëtchikov, Localization of One-Dimensional Random Walks in Random Environments, Harwood Academic Publishers, Chur, 1989. | MR

[14] A.V. Lëtchikov, 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. | MR | Zbl

[15] V.I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov exponents of dynamical systems, Trudy Moskov. Mat. Obšč. 19 (1968) 179-210. | MR | Zbl

[16] A. Raugi, Théorème ergodique multiplicatif. Produits de matrices aléatoires indépendantes, in: Fascicule de probabilités, Univ. Rennes I, 1997, pp. 43. | Zbl

[17] F. Solomon, Random walks in a random environment, Ann. Probab. 3 (1975) 1-31. | MR | Zbl

Cité par Sources :