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Keywords
(4)
Decay Rate
Length Scale
Two Dimensions
Invasion Percolation
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Outlets of 2D invasion percolation and multiplearmed incipient infinite clusters
Outlets of 2D invasion percolation and multiplearmed incipient infinite clusters,10.1007/s004400100274y,Probability Theory and Related Fields,Mich
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Outlets of 2D invasion percolation and multiplearmed incipient infinite clusters
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Citations: 2
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Michael Damron
,
Artëm Sapozhnikov
We study
invasion percolation
in two dimensions, focusing on properties of the outlets of the invasion and their relation to critical percolation and to incipient infinite clusters (IICs). First we compute the exact
decay rate
of the distribution of both the weight of the kth outlet and the volume of the kth pond. Next we prove bounds for all moments of the distribution of the number of outlets in an annulus. This result leads to almost sure bounds for the number of outlets in a box B(2 n ) and for the
decay rate
of the weight of the kth outlet to p c . We then prove existence of multiplearmed IIC measures for any number of arms and for any color sequence which is alternating or monochromatic. We use these measures to study the invaded region near outlets and near edges in the invasion backbone far from the origin.
Journal:
Probability Theory and Related Fields  PROBAB THEORY RELAT FIELD
, vol. 150, no. 1, pp. 257294, 2011
DOI:
10.1007/s004400100274y
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References
(25)
Proof Of The Van Den BergKesten Conjecture
(
Citations: 27
)
David Reimer
Journal:
Combinatorics, Probability & Computing  CPC
, vol. 9, no. 1, pp. 2732, 2000
The incipient infinite cluster in twodimensional percolation
(
Citations: 51
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Harry Kesten
Journal:
Probability Theory and Related Fields  PROBAB THEORY RELAT FIELD
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Scaling relations for 2 D percolation
(
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)
Harry Kesten
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 109, no. 1, pp. 109156, 1987
Large Deviations of Sums of Independent Random Variables
(
Citations: 128
)
S. V. Nagaev
Journal:
Annals of Probability  ANN PROBAB
, vol. 7, no. 1979, pp. 745789, 1979
Relations between invasion percolation and critical percolation in two dimensions
(
Citations: 2
)
Michael Damron
,
Artëm Sapozhnikov
,
Bálint Vágvölgyi
Journal:
Annals of Probability  ANN PROBAB
, vol. 37, no. 2009, pp. 22972331, 2009
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Citations
(2)
Pivotal, cluster and interface measures for critical planar percolation
(
Citations: 1
)
Christophe Garban
,
Gábor Pete
,
Oded Schramm
Published in 2010.
Limit theorems for 2D invasion percolation
Michael Damron
,
Artëm Sapozhnikov
Published in 2010.