Quenched, annealed and functional large deviations for one-dimensional random walk in random environment

Probability Theory and Related Fields

Volumn 118, Issue 1, 2000, Pages 65-114

  Comets, Francis ^a   Gantert, Nina ^b   Zeitouni, Ofer ^c  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Large deviations; Random walk in random environment

Indexed keywords

EID: 0034411530     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400000074     Document Type: Article

References (24)

1. Alili, S.: Asymptotic behaviour for random walks in random environments, J. Appl. Prob. 36, 334-349 (1999)
2. Chung, K.L.: Markov chains with stationary transition probabilities, Berlin, Springer, 1960
3. Dembo, A., Peres, Y., Zeitouni, O.: Tail estimates for one-dimensional random walk in random environment, Commun. Math. Phys. 181, 667-683 (1996)
4. Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications, second edition, Springer, New York (1998)
5. Dette, H., Fill, J.A., Pitman, J., Studden, W.J., Wall and Siegmund duality relations for birth and death chains with reflecting barrier, J. Theor. Prob. 10, 349-374 (1997)
6. Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time III, Comm. Pure Appl. Math. 29, 389-461 (1976)
7. Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time IV, Comm. Pure Appl. Math. 36, 183-212 (1983)
8. Föllmer, H.: Random fields and diffusion processes. In: Ecole d'Eté de Saint Flour XV-XVII, Springer Lect. Notes in Math. 1362, 101-203 (1988)
9. Gantert, N., Zeitouni, O.: Quenched sub-exponential tail estimates for one-dimensional random walk in random environment. Commun. Math. Phys. 194, 177-190 (1998)
10. Georgii, H.-O.: Gibbs Measures and Phase Transitions. De Gruyter, Berlin (1988)
11. Greven, A., den Hollander, F.: Large deviations for a random walk in random environment, Ann. Probab. 22, 1381-1428 (1994)
12. Hughes, B. D.: Random walks and random environments, Clarendon Press, Oxford (1996)
13. Jones, W.B., Thron, W.J.: Continued fractions, Encyclopedia of Mathematics and its Applications, vol. 11, Addison-Wesley, 1980
14. Kesten, H., Kozlov, M.V., Spitzer, F.: A limit law for random walk in a random environment, Comp. Math. 30, 145-168 (1975)
15. Kozlov, M. V.: Random walk in a one-dimensional random medium, Th. Prob. and Appl. 18, 387-388 (1973)
16. Ledrappier, F.: Quelques propriétés des exposants charactéristiques, Springer, LNM 1097, 305-396 (1984)
17. Pisztora, A., Povel, T.: Large deviation principle for random walk in a quenched environment in the low speed regime, Ann. Probab. 27, 1389-1413 (1999)
18. Pisztora, A., Povel, T., Zeitouni, O.: Precise large deviations estimates for one dimensional random walk in random environment, Probab. Theory Related Fields 113, 171-190 (1999)
19. Révész, P.: Random walk in random and non-random environments, World Scientific, Singapore (1990)
20. Solomon, F.: Random walks in random environment, Ann. Probab. 3, 1-31 (1975)
21. Spitzer, F.: Principles of random walk, Springer, Berlin (1976)
22. Sznitman, A.-S.: Slowdown and neutral pockets for a random walk in a random environment, Probab. Theory Related Fields 115, 287-323 (1999)
23. Wall, H.S.: Analytic theory of continued fractions, Van Nostrand, 1948
24. Zerner, M.P.W.: Lyapunov exponents and quenched large deviations for multi-dimensional random walk in random environment, Ann. Probab. 26, 1446-1476 (1998)