We consider a nearest-neighbor, one-dimensional random walk {
} in a random i.i.d. environment, in the regime where the walk is transient with speed
>0 and there exists an ∈(1, 2) such that the annealed law of
(
−
) converges to a stable law of parameter . Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible. In particular we show that there exist sequences {
...
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 that determines the fluctuations of the process. When , the averaged distributions of the hitting times of the random walk converge to a -stable distribution. However, it was shown recently that in this case there does not exist a quenched limiting distribution of the hitting times. That is, it is not true that for...
It is well known that the distribution of simple random walks on ℤ conditioned on returning to the origin after 2 steps does not depend on =(1=1), the probability of moving to the right. Moreover, conditioned on {2=0} the maximal displacement max≤2|
| converges in distribution when scaled by √ (diffusive scaling). We consider the analogous problem for transient random walks in random environments on ℤ. We show that under the quenched law
(conditioned on the environment...
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