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- W3158057521 abstract "We examine a class of random walks in random environments on $mathbb{Z}$ with bounded jumps, a generalization of the classic one-dimensional model. The environments we study have i.i.d. transition probability vectors drawn from Dirichlet distributions. For this model, we characterize recurrence and transience, and in the transient case we characterize ballisticity. For ballisticity, we give two parameters, $kappa_0$ and $kappa_1$. The parameter $kappa_0$ governs finite trapping effects, and $kappa_1$ governs repeated traversals of arbitrarily large regions of the graph. We show that the walk is right-transient if and only if $kappa_1>0$, and in that case it is ballistic if and only if $min(kappa_0,kappa_1)>1$." @default.
- W3158057521 created "2021-05-10" @default.
- W3158057521 creator A5083133330 @default.
- W3158057521 date "2021-04-30" @default.
- W3158057521 modified "2023-09-27" @default.
- W3158057521 title "Random Walks in Dirichlet Random Environments on $mathbb{Z}$ with Bounded Jumps" @default.
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