Article ID Journal Published Year Pages File Type
1156102 Stochastic Processes and their Applications 2009 21 Pages PDF
Abstract

We consider random walk with a nonzero bias to the right, on the infinite cluster in the following percolation model: take i.i.d. bond percolation with retention parameter pp on the so-called infinite ladder, and condition on the event of having a bi-infinite path from −∞−∞ to ∞∞. The random walk is shown to be transient, and to have an asymptotic speed to the right which is strictly positive or zero depending on whether the bias is below or above a certain critical value which we compute explicitly.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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