TY - JOUR
T1 - On slowdown and speedup of transient random walks in random environment
AU - Fribergh, Alexander
AU - Gantert, Nina
AU - Popov, Serguei
PY - 2010/2
Y1 - 2010/2
N2 - We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(nκ) from the origin, κ ∈ (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order O(nν 0 from the origin, ν0 ∈ (0, κ)), and speedup (at time n, the particle is at a distance of order nν 1 from the origin, ν1 ∈ (κ, 1)), for the current location of the particle and for the hitting times. Also, we study probabilities of backtracking: at time n, the particle is located around (-nν), thus making an unusual excursion to the left. For the slowdown, our results are valid in the ballistic case as well.
AB - We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(nκ) from the origin, κ ∈ (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order O(nν 0 from the origin, ν0 ∈ (0, κ)), and speedup (at time n, the particle is at a distance of order nν 1 from the origin, ν1 ∈ (κ, 1)), for the current location of the particle and for the hitting times. Also, we study probabilities of backtracking: at time n, the particle is located around (-nν), thus making an unusual excursion to the left. For the slowdown, our results are valid in the ballistic case as well.
KW - Moderate deviations
KW - Slowdown
KW - Speedup
KW - Transience
UR - http://www.scopus.com/inward/record.url?scp=76949089063&partnerID=8YFLogxK
U2 - 10.1007/s00440-009-0201-2
DO - 10.1007/s00440-009-0201-2
M3 - Article
AN - SCOPUS:76949089063
SN - 0178-8051
VL - 147
SP - 43
EP - 88
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 1
ER -