On the concentration of Sinai's walk

Pierre Andreoletti

Stochastic Processes and their Applications, 2006, vol. 116, issue 10, 1377-1408

Abstract: 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.

Keywords: Random; environment; Random; walk; Sinai's; regime; Markov; chain; Local; time (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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