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. 
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/
@article{DM_2023_35_4_a0,
     author = {G. A. Bakai},
     title = {Large {Deviations} for {First} {Hitting} time of {Random} {Walk} in {Random} {Environment} (lower level)},
     journal = {Diskretnaya Matematika},
     pages = {3--17},
     year = {2023},
     volume = {35},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2023_35_4_a0/}
}
TY  - JOUR
AU  - G. A. Bakai
TI  - Large Deviations for First Hitting time of Random Walk in Random Environment (lower level)
JO  - Diskretnaya Matematika
PY  - 2023
SP  - 3
EP  - 17
VL  - 35
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/DM_2023_35_4_a0/
LA  - ru
ID  - DM_2023_35_4_a0
ER  - 
%0 Journal Article
%A G. A. Bakai
%T Large Deviations for First Hitting time of Random Walk in Random Environment (lower level)
%J Diskretnaya Matematika
%D 2023
%P 3-17
%V 35
%N 4
%U http://geodesic.mathdoc.fr/item/DM_2023_35_4_a0/
%G ru
%F DM_2023_35_4_a0

[1] Solomon F., “Random walks in a random environment”, Ann. Probab., 3:1 (1975), 1–31 | DOI | MR | Zbl

[2] Kesten H., Kozlov M. V., Spitzer F., “A limit law for random walk in a random environment”, Compos. Math., 30:2 (1975), 145–168 | MR | Zbl

[3] Comets F., Gantert N., Zeitouni O., “Quenched, annealed and functional large deviations for one-dimensional random walk in random environment”, Probab. Theory Relat. Fields, 118:1 (2000), 65–114 | DOI | MR | Zbl

[4] Afanasev V. I., “Dvugranichnaya zadacha dlya sluchainogo bluzhdaniya v sluchainoi srede”, Teoriya veroyatn. i ee primen., 63:3 (2018), 417–430 | DOI

[5] Greven A., den Hollander F., “Large deviations for a random walk in random environment”, Ann. Probab., 22:3 (1994), 1381–1428 | DOI | MR | Zbl

[6] Dembo A., Peres Y., Zeitouni O., “Tail estimates for one-dimensional random walk in random environment”, Comm. Math. Physics, 181:3 (1996), 667–683 | DOI | MR | Zbl

[7] Mogulskii A. A., “Lokalnye teoremy dlya arifmeticheskikh obobschennykh protsessov vosstanovleniya pri vypolnenii usloviya Kramera”, Sib. elektr. matem. izv., 16 (2019), 21–41 | MR | Zbl

[8] Bakai G. A., “O kharakterizatsii veroyatnostei bolshikh uklonenii dlya regeneriruyuschikh posledovatelnostei”, Trudy MIAN, 316 (2022), 47–63 | DOI | MR

[9] Schaefer H. H., “Some spectral properties of positive linear operators”, Pacific J. Math., 10:3 (1960), 1009–1019 | DOI | MR | Zbl

[10] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972, 740 pp. | MR

[11] Marek I., “Frobenius theory of positive operators: comparison theorems and applications”, SIAM J. Appl. Math., 19:3 (1970), 607–628 | DOI | MR | Zbl

[12] Bakai G. A., “O bolshikh ukloneniyakh momenta dostizheniya dalekogo urovnya sluchainym bluzhdaniem v sluchainoi srede”, Diskretnaya matematika, 34:4 (2022), 3–13 | DOI

[13] Bakai G. A., “Bolshie ukloneniya dlya obryvayuschegosya obobschennogo protsessa vosstanovleniya”, Teoriya veroyatn. i ee primen., 66:2 (2021), 261–283 | DOI | MR

[14] Schaefer H. H., “On the point spectrum of positive operators”, Proc. Amer. Math. Soc., 15:1 (1964), 56–60 | DOI | MR | Zbl