Quenched limits for transient, zero speed one-dimensional random walk in random environment
نویسندگان
چکیده
منابع مشابه
Quenched Limits for Transient, Zero Speed One-Dimensional Random Walk in Random Environment
We consider a nearest-neighbor, one dimensional random walk {Xn}n≥0 in a random i.i.d. environment, in the regime where the walk is transient but with zero speed, so thatXn is of order n for some s < 1. Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible: there exist sequences {nk} and {xk} depending on the environment only, such that Xnk − xk ...
متن کاملQuenched limits for transient, ballistic, sub-Gaussian one-dimensional random walk in random environment
We consider a nearest-neighbor, one-dimensional random walk {Xn}n≥0 in a random i.i.d. environment, in the regime where the walk is transient with speed vP > 0 and there exists an s ∈ (1,2) such that the annealed law of n−1/s(Xn − nvP ) converges to a stable law of parameter s. Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible. In particular ...
متن کاملWeak Quenched Limiting Distributions for Transient One-dimensional Random Walk in a Random Environment
We consider a one-dimensional, transient random walk in a random i.i.d. environment. The asymptotic behaviour of such random walk depends to a large extent on a crucial parameter κ > 0 that determines the fluctuations of the process. When 0 < κ < 2, the averaged distributions of the hitting times of the random walk converge to a κ-stable distribution. However, it was shown recently that in this...
متن کاملQuenched sub{exponential tail estimates for one-dimensional random walk in random environment
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment deenes a random walk fX n g (called a RWRE) which, when at x, moves one step to the right with probability ! x , and one step to the left with probability 1?! x. Solomon (1975) determined the almost-sure asymptotic speed v (=rate of escape) ...
متن کاملQuenched, Annealed and Functional Large Deviations for One-Dimensional Random Walk in Random Environment
Suppose that the integers are assigned random variables f! i g (taking values in the unit interval), which serve as an environment. This environment deenes a random walk fX n g (called a RWRE) which, when at i, moves one step to the right with probability ! i , and one step to the left with probability 1 ? ! i. When the f! i g sequence is i.i.d., Greven and den Hollander (1994) proved a large d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2009
ISSN: 0091-1798
DOI: 10.1214/08-aop399