Geodesic
Large Deviations for First Hitting time of Random Walk in Random Environment (lower level)
Diskretnaya Matematika, Tome 35 (2023) no. 4, pp. 3-17.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $T_{-n}$, $n \in\mathbb{N}$, be a hitting time of level -n for a random walk in random environment (RWRE). The exact asymptotics $P(T_{-n} = k)$ are proved. Here $k =k(n)$, $n$-k is even for every n and the ratio $k/n$ belongs to a compact set.
Keywords: local limit theorems, large deviations, random walk in random environment, improper regeneration. 
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G. A. Bakai. Large Deviations for First Hitting time of Random Walk in Random Environment (lower level). Diskretnaya Matematika, Tome 35 (2023) no. 4, pp. 3-17. http://geodesic.mathdoc.fr/item/DM_2023_35_4_a0/

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