Biased random walk in a one-dimensional percolation model

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

percolation

random walk

asymptotic speed

asymptotic speed

Publikations- och innehållstyp

ref (ämneskategori)

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