On the concentration of Sinai’s walk

@inproceedings{Andreoletti2005OnTC,
  title={On the concentration of Sinai’s walk},
  author={Pierre Andreoletti},
  year={2005}
}
We consider Sinai's random walk in a random environment. We prove that for an interval of time [1,n] Sinai's walk sojourns in a small neighborhood of the point of localization for the quasi-totality of this amount of time. Moreover the local time at the point of localization normalized by n converges in probability to a well defined random variable of the environment. From these results we get applications to the favorite sites of the walk and to the maximum of the local time. 

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References

Publications referenced by this paper.
SHOWING 1-10 OF 14 REFERENCES

Random Walks in a Random Environment

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Precise estimates for the concentration neighbourhood of Sinai’s

2004a. P. Andreoletti
  • walk. Preprint,
  • 1967
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Alternative proof for the localisation of Sinai’s

Ann. Probab, 2004. P. Andreoletti
  • walk. to appear in Journal of Statistical Physics,
  • 2004

Localization of a diffusion process in a one-dimensional brownian environmement

H. Tanaka
  • Processes and their applications,
  • 2002