Details

Autor(en) / Beteiligte

• COMETS, Francis
• POPOV, Serguei

Titel

Limit law for transition probabilities and moderate deviations for Sinai's random walk in random environment

Ist Teil von

• Probability theory and related fields, 2003-08, Vol.126 (4), p.571-609

Ort / Verlag

Heidelberg: Springer

Erscheinungsjahr

2003

Quelle

EBSCOhost Business Source Ultimate

Beschreibungen/Notizen

• We consider a one-dimensional random walk in random environment in the Sinai's regime. Our main result is that logarithms of the transition probabilities, after a suitable rescaling, converge in distribution as time tends to infinity, to some functional of the Brownian motion. We compute the law of this functional when the initial and final points agree. Also, among other things, we estimate the probability of being at time <t< at distance at least <z< from the initial position, when <z< is larger than ln<2<<t<, but still of logarithmic order in time.