Random walk on the high-dimensional IIC

Onderzoeksoutput: Boek/rapportRapportAcademic

Uittreksel

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.
Originele taal-2Engels
Uitgeverijs.n.
Aantal pagina's36
StatusGepubliceerd - 2012

Publicatie series

NaamarXiv.org
Volume1207.7230 [math.PR]

Vingerafdruk

Random walk
High-dimensional
Range of data
Euclidean
Ball
Effective Resistance
Exit Time
Backbone
Higher Dimensions
Asymptotic Behavior

Citeer dit

Heydenreich, M. O., Hofstad, van der, R. W., & Hulshof, W. J. T. (2012). Random walk on the high-dimensional IIC. (arXiv.org; Vol. 1207.7230 [math.PR]). s.n.
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title = "Random walk on the high-dimensional IIC",
abstract = "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.",
author = "M.O. Heydenreich and {Hofstad, van der}, R.W. and W.J.T. Hulshof",
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Heydenreich, MO, Hofstad, van der, RW & Hulshof, WJT 2012, 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.

s.n., 2012. 36 blz. (arXiv.org; Vol. 1207.7230 [math.PR]).

Onderzoeksoutput: Boek/rapportRapportAcademic

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 -

Heydenreich MO, Hofstad, van der RW, Hulshof WJT. Random walk on the high-dimensional IIC. s.n., 2012. 36 blz. (arXiv.org).