### Uittreksel

Originele taal-2 | Engels |
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Uitgeverij | s.n. |

Aantal pagina's | 36 |

Status | Gepubliceerd - 2012 |

### Publicatie series

Naam | arXiv.org |
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Volume | 1207.7230 [math.PR] |

### Vingerafdruk

### Citeer dit

*Random walk on the high-dimensional IIC*. (arXiv.org; Vol. 1207.7230 [math.PR]). s.n.

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*Random walk on the high-dimensional IIC*. arXiv.org, vol. 1207.7230 [math.PR], s.n.

**Random walk on the high-dimensional IIC.** / Heydenreich, M.O.; Hofstad, van der, R.W.; Hulshof, W.J.T.

Onderzoeksoutput: Boek/rapport › Rapport › Academic

TY - BOOK

T1 - Random walk on the high-dimensional IIC

AU - Heydenreich, M.O.

AU - Hofstad, van der, R.W.

AU - Hulshof, W.J.T.

PY - 2012

Y1 - 2012

N2 - We study the asymptotic behavior the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by [26]. We do this by obtaining bounds on the effective resistance between the origin and the boundary of these Euclidean balls. We show that the geometric properties of long-range percolation clusters are significantly different from those of finite-range clusters. We also study the behavior of random walk on the backbone of the IIC and we prove that the Alexander-Orbach conjecture holds for the incipient infinite cluster in high dimensions, both for long-range percolation and for finite-range percolation.

AB - We study the asymptotic behavior the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by [26]. We do this by obtaining bounds on the effective resistance between the origin and the boundary of these Euclidean balls. We show that the geometric properties of long-range percolation clusters are significantly different from those of finite-range clusters. We also study the behavior of random walk on the backbone of the IIC and we prove that the Alexander-Orbach conjecture holds for the incipient infinite cluster in high dimensions, both for long-range percolation and for finite-range percolation.

M3 - Report

T3 - arXiv.org

BT - Random walk on the high-dimensional IIC

PB - s.n.

ER -