Process-level quenched large deviations for random walk in random environment
Firas Rassoul-Agha; Timo Seppäläinen
Annales de l'I.H.P. Probabilités et statistiques (2011)
- Volume: 47, Issue: 1, page 214-242
- ISSN: 0246-0203
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] C. Boldrighini, R. A. Minlos and A. Pellegrinotti. Random walks in quenched i.i.d. space–time random environment are always a.s. diffusive. Probab. Theory Related Fields 129 (2004) 133–156. Zbl1062.60044MR2052866
- [2] F. Comets, N. Gantert and O. Zeitouni. Quenched, annealed and functional large deviations for one-dimensional random walk in random environment. Probab. Theory Related Fields 118 (2000) 65–114. Zbl0965.60098MR1785454
- [3] A. Dembo and O. Zeitouni. Large Deviations Techniques and Applications, 2nd edition. Applications of Mathematics 38. Springer, New York, 1998. Zbl0896.60013MR1619036
- [4] F. den Hollander. Large Deviations. Fields Institute Monographs 14. Amer. Math. Soc., Providence, RI, 2000. Zbl0949.60001MR1739680
- [5] J.-D. Deuschel and D. W. Stroock. Large Deviations. Pure and Applied Mathematics 137. Academic Press, Boston, MA, 1989. Zbl0705.60029MR997938
- [6] M. D. Donsker and S. R. S. Varadhan. Asymptotic evaluation of certain Markov process expectations for large time. I. Comm. Pure Appl. Math. 28 (1975) 1–47. Zbl0323.60069MR386024
- [7] M. D. Donsker and S. R. S. Varadhan. Asymptotic evaluation of certain Markov process expectations for large time. III. Comm. Pure Appl. Math. 29 (1976) 389–461. Zbl0348.60032MR428471
- [8] I. Ekeland and R. Témam. Convex Analysis and Variational Problems, English edition. Classics in Applied Mathematics 28. SIAM, Philadelphia, PA, 1999. Zbl0939.49002MR1727362
- [9] H.-O. Georgii. Gibbs Measures and Phase Transitions. de Gruyter Studies in Mathematics 9. Walter de Gruyter, Berlin, 1988. Zbl0657.60122MR956646
- [10] A. Greven and F. den Hollander. Large deviations for a random walk in random environment. Ann. Probab. 22 (1994) 1381–1428. Zbl0820.60054MR1303649
- [11] G. Kassay. A simple proof for König’s minimax theorem. Acta Math. Hungar. 63 (1994) 371–374. Zbl0811.90115MR1261480
- [12] E. Kosygina, F. Rezakhanlou and S. R. S. Varadhan. Stochastic homogenization of Hamilton–Jacobi–Bellman equations. Comm. Pure Appl. Math. 59 (2006) 1489–1521. Zbl1111.60055MR2248897
- [13] F. Rassoul-Agha. The point of view of the particle on the law of large numbers for random walks in a mixing random environment. Ann. Probab. 31 (2003) 1441–1463. Zbl1039.60089MR1989439
- [14] F. Rassoul-Agha and T. Seppäläinen. An almost sure invariance principle for random walks in a space–time random environment. Probab. Theory Related Fields 133 (2005) 299–314. Zbl1088.60094MR2198014
- [15] F. Rassoul-Agha and T. Seppäläinen. A course on large deviation theory with an introduction to Gibbs measures. Preprint, 2009. Zbl1330.60001MR2521407
- [16] M. Rosenblatt. Markov Processes. Structure and Asymptotic Behavior. Springer, New York, 1971. Zbl0236.60002MR329037
- [17] J. Rosenbluth. Quenched large deviations for multidimensional random walk in random environment: A variational formula. Thesis dissertation, New York University, 2006. Available at http://arxiv.org/abs/0804.1444. MR2708406
- [18] W. Rudin. Functional Analysis, 2nd edition. McGraw-Hill, New York, 1991. Zbl0253.46001MR1157815
- [19] T. Seppäläinen. Large deviations for lattice systems. I. Parametrized independent fields. Probab. Theory Related Fields 96 (1993) 241–260. Zbl0792.60025MR1227034
- [20] D. W. Stroock and S. R. S. Varadhan. Multidimensional Diffusion Processes. Springer, Berlin, 2006. Zbl1103.60005MR2190038
- [21] S. R. S. Varadhan. Large Deviations and Applications. CBMS-NSF Regional Conference Series in Applied Mathematics 46. SIAM, Philadelphia, PA, 1984. Zbl0549.60023MR758258
- [22] S. R. S. Varadhan. Large deviations for random walks in a random environment. Comm. Pure Appl. Math. 56 (2003) 1222–1245. Dedicated to the memory of Jürgen K. Moser. Zbl1042.60071MR1989232
- [23] A. Yilmaz. Large deviations for random walk in a space–time product environment. Ann. Probab. 37 (2009a) 189–205. Zbl1159.60355MR2489163
- [24] A. Yilmaz. Quenched large deviations for random walk in a random environment. Comm. Pure Appl. Math. 62 (2009b) 1033–1075. Zbl1168.60370MR2531552
- [25] M. P. W. Zerner. Lyapounov exponents and quenched large deviations for multidimensional random walk in random environment. Ann. Probab. 26 (1998) 1446–1476. Zbl0937.60095MR1675027