# 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.

#### Citations

##### Publications citing this paper.

SHOWING 1-9 OF 9 CITATIONS

## Sinai's Walk : a Statistical Aspect (preliminary Version)

VIEW 8 EXCERPTS

CITES METHODS, BACKGROUND & RESULTS

## Random walks in random environment on Z: localization studies in the recurrent and transient cases

VIEW 9 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Sinai's walk: a statistical aspect

VIEW 9 EXCERPTS

CITES RESULTS, METHODS & BACKGROUND

## Hidden Markov model for parameter estimation of a random walk in a Markov environment

VIEW 4 EXCERPTS

CITES BACKGROUND & METHODS

## Parametric estimation of a one-dimensional ballistic random walk in a Markov environment

VIEW 4 EXCERPTS

CITES BACKGROUND & METHODS

## Spider walk in a random environment

VIEW 1 EXCERPT

CITES BACKGROUND

## Random Walks in a Sparse Random Environment

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 14 REFERENCES

## The problem of the most visited site in random environment

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Random Walks in a Random Environment

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Precise estimates for the concentration neighbourhood of Sinai’s

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL