Upper limits of Sinai's walk in random scenery
Probability
2007-11-08 v2
Abstract
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.
Cite
@article{arxiv.math/0610326,
title = {Upper limits of Sinai's walk in random scenery},
author = {Olivier Zindy},
journal= {arXiv preprint arXiv:math/0610326},
year = {2007}
}
Comments
29 pages