Upper limits of Sinai's walk in random scenery

Details Upper limits of Sinai's walk in random scenery Upper limits of Sinai's walk in random scenery

2006-10-10

arxiv.org/abs/math/0610326v2

Mathematics

Probability

29 pages

Scientific paper

We consider Sinai's walk in i.i.d. random scenery and focus our attention on a conjecture of R\'ev\'esz \cite{r05} concerning the upper limits of Sinai's walk in random scenery when the scenery is bounded from above. A close study of the competition between the concentration property for Sinai's walk and negative values for the scenery enables us to prove that the conjecture is true if the scenery has "thin" negative tails and is false otherwise.

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