Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60J15 Random walks
- 60J60 Diffusion processes, See also {58G32}
- 60F05 Central limit and other weak theorems

**Résumé:** Consider a class of diffusions with random potentials which
asymptotically behave as a Brownian motion, we study the
tightness of localization around the bottom of some Brownian
valley, and determine the limit distribution of their return
time to the origin after a typical time. Via the Skorokhod
embedding in random environment, we also solve the return
time problem for Sinai's walk.

**Mots Clés:** *Tightness of localization; return time; valley; diffusion with random potential; Sinai's walk in random environment*

**Date:** 1999-03-29

**Prépublication numéro:** *PMA-496*