Random walk on the incipient infinite cluster for oriented percolation in high dimensions

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dc.creatorBarlow, Martin T.
dc.creatorJarai, Antal A.
dc.creatorKumagai, Takashi
dc.creatorSlade, Gordon
dc.date2006-08-07
dc.date2007-09-01
dc.date.accessioned2026-07-07T08:26:46Z
dc.date.available2026-07-07T08:26:46Z
dc.descriptionWe consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation on $Z^d \times Z_+$. In dimensions $d>6$, we obtain bounds on exit times, transition probabilities, and the range of the random walk, which establish that the spectral dimension of the incipient infinite cluster is 4/3, and thereby prove a version of the Alexander--Orbach conjecture in this setting. The proof divides into two parts. One part establishes general estimates for simple random walk on an arbitrary infinite random graph, given suitable bounds on volume and effective resistance for the random graph. A second part then provides these bounds on volume and effective resistance for the incipient infinite cluster in dimensions $d>6$, by extending results about critical oriented percolation obtained previously via the lace expansion.
dc.description48 pages
dc.identifierhttps://arxiv.org/abs/math/0608164
dc.identifierhttp://arxiv.org/abs/math/0608164
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137053
dc.subjectProbability
dc.subjectMathematical Physics
dc.titleRandom walk on the incipient infinite cluster for oriented percolation in high dimensions
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