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Biased random walk in a one-dimensional percolation model

Marina Axelson-Fisk (Institutionen för matematiska vetenskaper, matematisk statistik) ; Olle Häggström (Institutionen för matematiska vetenskaper, matematisk statistik)
Stochastic processes and their Applications (0304-4149). Vol. 119 (2009), 10, p. 3395-3415.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: percolation, random walk, asymptotic speed

Denna post skapades 2009-12-01. Senast ändrad 2017-07-03.
CPL Pubid: 102518


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)


Matematisk statistik

Chalmers infrastruktur