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Creators/Authors contains: "Slonim, Daniel J."

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  1. (, Latin American Journal of Probability and Mathematical Statistics)
    We examine a class of random walks in random environments on 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 the transient case of this model, we characterize ballisticity: nonzero limiting velocity. We do this in terms of two parameters, κ0 and κ1. The parameter κ0 governs finite trapping effects. The parameter κ1, which already is known to characterize directional transience, also governs repeated traversals of arbitrarily large regions of the graph. We show that the walk is ballistic if and only if min(κ0, κ1) > 1. We prove some stronger results regarding moments of the quenched Green function and other functions that the quenched Green function dominates. These results help us to better understand the phenomena and parameters affecting ballisticity. 
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  2. (, Markov processes and related fields)
    We characterize ballistic behavior for general i.i.d. random walks in random envi- ronments on Z with bounded jumps. The two characterizations we provide do not use uniform ellipticity conditions. They are natural in the sense that they both relate to formulas for the limiting speed in the nearest-neighbor case. 
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    Accepted Manuscript Full Text Available
  3. ; ; (, Advances in Applied Mathematics)
    null (Ed.)
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