Proceedings Mathematical Sciences

, Volume 114, Issue 4, pp 309–318 | Cite as

Random walks in a random environment

  • S. R. S. Varadhan
Invited Articles


Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the ‘quenched’ and the ‘averaged’ case.


Large deviations random walks in a random environment 


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  1. [1]
    Bricmont J and Kupiainen A, Random walks in asymmetric random environments,Comm. Math. Phys. 142(2) (1991) 345–420MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Comets Francis, Gantert Nina and Zeitouni Ofer, Quenched, annealed and functional large deviations for one-dimensional random walk in random environment,Probab. Theory Related Fields 118(1) (2000) 65–114MATHMathSciNetGoogle Scholar
  3. [3]
    Greven Andreas and den Hollander Frank, Large deviations for a random walk in random environment,Ann. Probab. 22(3) (1994) 1381–1428MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Kosygina E, Rezakhnalou F and Varadhan S R S, Homogenization of random Hamilton-Jacobi-Bellman equations (in preparation)Google Scholar
  5. [5]
    Sinai Ya G, The limit behavior of a one-dimensional random walk in a random environment,Theor. Probab. Appl. 27(2) (1982) 256–268CrossRefMathSciNetGoogle Scholar
  6. [6]
    Solomon Fred, Random walks in a random environment,Ann. Probab. 3 (1975) 1–31MATHCrossRefGoogle Scholar
  7. [7]
    Sznitman A S and Zeitouni O, On the diffusive behavior of isotropic diffusions in a random environment,C. R. Acad. Sci. Paris, Ser. I 339 (2004) 429–434MATHMathSciNetGoogle Scholar
  8. [8]
    Varadhan S R S, Large deviations for random walks in a random environment. Dedicated to the memory of Jürgen K Moser,Comm. Pure Appl. Math. 56(8) (2003) 1222–1245MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Zeitouni Ofer, Random walks in random environments, Proceedings of ICM 2002, vol. III, pp.117–127Google Scholar
  10. [10]
    Zeitouni Ofer, Lecture Notes on RWRE, Notes from the St. Flour Summer School in Probability (2001), available at Scholar
  11. [11]
    Zerner Martin P W, Lyapunov exponents and quenched large deviations for multidimensional random walk in random environment,Ann. Probab. 26(4) (1998) 1446–1476MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Indian Academy of Sciences 2004

Authors and Affiliations

  1. 1.Department of Mathematics, Courant Institute of Mathematical SciencesNew York UniversityUSA

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