Non-perturbative approach to random walk in markovian environment

Dmitry Dolgopyat (University of Maryland)
Carlangelo Liverani (Universito of Rome 2)

Abstract


We prove the CLT for a random walk in a dynamical environment where the states of the environment at different sites are independent Markov chains.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 245-251

Publication Date: June 4, 2009

DOI: 10.1214/ECP.v14-1467

References

  1. J. Aaronson. An introduction to infinite ergodic theory. Mathematical Surveys and Monographs, 50. American Mathematical Society, Providence, RI, 1997. Math. Review 99d:28025
  2. A. Bandyopadhyay, O. Zeitouni. Random Walk in Dynamic Markovian Random Environment, ALEA 1 (2006) 205--224. Math. Review 2007e:60097
  3. C. Boldrighini, R.A. Minlos, A. Pellegrinotti. Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive. Probab. Theory Related Fields 129 (2004), no. 1, 133--156. Math. Review 2005e:60048
  4. C. Boldrighini, R.A. Minlos, A. Pellegrinotti. Random walks in random (fluctuating) environment. Russian Math Surveys 62(2007) 663--712. Math. Review 2358736
  5. E. Bolthausen, A.--S. Sznitman. On the static and dynamic points of view for certain random walks in random environment. Methods Appl. Anal. 9, 3, 345--375 (2002). Math. Review 2005c:60133
  6. F. Comets, O. Zeitouni. Gaussian fluctuations for random walks in random mixing environments. Israel J. Math. 148(2005), 87--113. Math. Review 2006k:60179
  7. D. Dolgopyat, G. Keller, C. Liverani. Random Walk in Markovian Environment. Annals of Probability 36 (2008) 1676--1710. Math. Review 2009f:60124
  8. D. Dolgopyat, C. Liverani. Random Walk in Deterministically Changing Environment. ALEA 4(2008) 89--116. Math. Review 2009e:82079
  9. G. K. Eagleson. Some simple conditions for limit theorems to be mixing. (Russian) Teor. Verojatnost. i Primenen 21(1976), no. 3, 653--660. (Engligh translation: Theor. Prob. Appl. 21 (1976) 637--642, 1977.) Math. Review 55 #1409
  10. W. Parry, M. Pollicott. Zeta functions and the periodic orbit structure of hyperbolic dynamics. Asterisque 187--188 (1990) 268 pp. Math. Review 92f:58141
  11. F. Rassoul-Agha, T. Seppalainen. An almost sure invariance principle for random walks in a space-time i.i.d. random environment. Prob. Th., Related Fields 133 (2005) 299--314. Math. Review 2007f:60030
  12. A. Renyi. On mixing sequences of sets. Acta math. Acad. Sci. Hungar. 9(1958). Math. Review 20 #4623
  13. D. Ruelle. Statistical mechanics. Rigorous results. Reprint of the 1989 edition. World Scientific Publishing Co., Inc., River Edge, NJ; Imperial College Press, London, 1999. Math. Review 44 #6279
  14. W. Stannat. A remark on the CLT for a random walk in a random environment. Probability Theory and Related Fields 130,3, 377-387 (2004). Math. Review 2005f:60063
  15. R. Zweimuller. Mixing limit theorems for ergodic transformations. Journal of Theoretical Probability 20 (2007), 1059-1071. Math. Review 2008h:60119


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.