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Weak quenched limiting distributions for transient one-dimensional random walk in a random environment
[article]

2016
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arXiv
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pre-print

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 case there does not exist a quenched limiting distribution of the hitting times. That is, it is not true

arXiv:1011.6366v4
fatcat:6uhvuc7375a2zp3x6tdyucm3xi