• Mathematics
• Published 2005
• DOI:10.1016/j.spa.2004.12.008

On the concentration of Sinai’s walk

@inproceedings{Andreoletti2005OnTC,
  title={On the concentration of Sinai’s walk},
  author={Pierre Andreoletti},
  year={2005}
}

• Pierre Andreoletti

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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.