Biased random walk in a one-dimensional percolation model Artikel i vetenskaplig tidskrift, 2009

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 $p$ on the so-called infinite ladder, and condition on the event of having a bi-infinite path from $-\infty$ to $\infty$. The random walk is shown to be transient, and to have an asymptotic speed to the right which strictly positive or zero depending on whether the bias is below or above a certain critical value which we compute explicitly.

asymptotic speed

percolation

random walk

Författare

Marina Axelson-Fisk

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet

Olle Häggström

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Stochastic Processes and their Applications

0304-4149 (ISSN)

Vol. 119 10 3395-3415

Ämneskategorier

Sannolikhetsteori och statistik

DOI

10.1016/j.spa.2009.06.004