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Citation(s) in
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1
Fully-connected bond percolation on $${\mathbb {Z}}^d$$.
Probab Theory Relat Fields
2021. [DOI:
10.1007/s00440-021-01088-8
]
[
Citation(s) in
RCA
: 1
]
[
Impact Index Per Article: 0.3
]
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[Indexed: 10/20/2022]
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2
Basu D
, Sapozhnikov A. Kesten’s incipient infinite cluster and quasi-multiplicativity of crossing probabilities.
ELECTRONIC COMMUNICATIONS IN PROBABILITY
2017. [DOI:
10.1214/17-ecp56
]
[
Citation(s) in
RCA
: 2
]
[
Impact Index Per Article: 0.3
]
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[Indexed: 11/19/2022]
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3
Fitzner R
, van der Hofstad R. Mean-field behavior for nearest-neighbor percolation in $d>10$.
ELECTRON J PROBAB
2017. [DOI:
10.1214/17-ejp56
]
[
Citation(s) in
RCA
: 30
]
[
Impact Index Per Article: 4.3
]
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[Indexed: 11/19/2022]
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4
Axelson-Fisk M
, Häggström O. Conditional percolation on one-dimensional lattices.
ADV APPL PROBAB
2016. [DOI:
10.1239/aap/1261669588
]
[
Citation(s) in
RCA
: 3
]
[
Impact Index Per Article: 0.4
]
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[Indexed: 11/18/2022]
Abstract
Conditioning independent and identically distributed bond percolation with retention parameter
p
on a one-dimensional periodic lattice on the event of having a bi-infinite path from -∞ to ∞ is shown to make sense, and the resulting model exhibits a Markovian structure that facilitates its analysis. Stochastic monotonicity in
p
turns out to fail in general for this model, but a weaker monotonicity property does hold: the average edge density is increasing in
p
.
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5
Conditional percolation on one-dimensional lattices.
ADV APPL PROBAB
2016. [DOI:
10.1017/s0001867800003761
]
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Citation(s) in
RCA
: 1
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[
Impact Index Per Article: 0.1
]
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[Indexed: 11/07/2022]
Abstract
Conditioning independent and identically distributed bond percolation with retention parameter
p
on a one-dimensional periodic lattice on the event of having a bi-infinite path from -∞ to ∞ is shown to make sense, and the resulting model exhibits a Markovian structure that facilitates its analysis. Stochastic monotonicity in
p
turns out to fail in general for this model, but a weaker monotonicity property does hold: the average edge density is increasing in
p
.
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MESH Headings
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6
Hammond A
, Pete G, Schramm O. Local time on the exceptional set of dynamical percolation and the incipient infinite cluster.
ANN PROBAB
2015. [DOI:
10.1214/14-aop950
]
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Citation(s) in
RCA
: 10
]
[
Impact Index Per Article: 1.1
]
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[Indexed: 11/19/2022]
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7
Benjamini I
, Duminil-Copin H, Kozma G, Yadin A. Disorder, entropy and harmonic functions.
ANN PROBAB
2015. [DOI:
10.1214/14-aop934
]
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Citation(s) in
RCA
: 26
]
[
Impact Index Per Article: 2.9
]
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[Indexed: 11/19/2022]
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8
Kiss D
. Large deviation bounds for the volume of the largest cluster in 2D critical percolation.
ELECTRONIC COMMUNICATIONS IN PROBABILITY
2014. [DOI:
10.1214/ecp.v19-3438
]
[
Citation(s) in
RCA
: 3
]
[
Impact Index Per Article: 0.3
]
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[Indexed: 11/19/2022]
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Affiliation(s)
Demeter Kiss
Cambridge University and Tohoku University
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9
van den Berg J
, Conijn R. The gaps between the sizes of large clusters in 2D critical percolation.
ELECTRONIC COMMUNICATIONS IN PROBABILITY
2013. [DOI:
10.1214/ecp.v18-3065
]
[
Citation(s) in
RCA
: 2
]
[
Impact Index Per Article: 0.2
]
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[Indexed: 11/19/2022]
Abstract
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Affiliation(s)
Jacob van den Berg
Centrum Wiskunde & Informatica
Rene Conijn
VU University Amsterdam
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10
Yao C
. A CLT for winding angles of the arms for critical planar percolation.
ELECTRON J PROBAB
2013. [DOI:
10.1214/ejp.v18-2285
]
[
Citation(s) in
RCA
: 2
]
[
Impact Index Per Article: 0.2
]
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[Indexed: 11/19/2022]
Abstract
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Affiliation(s)
Changlong Yao
Chinese Academy of Mathematics and Systems Science
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11
van den Berg J
, Conijn R. On the size of the largest cluster in 2D critical percolation.
ELECTRONIC COMMUNICATIONS IN PROBABILITY
2012. [DOI:
10.1214/ecp.v17-2263
]
[
Citation(s) in
RCA
: 2
]
[
Impact Index Per Article: 0.2
]
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[Indexed: 11/19/2022]
Abstract
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Affiliation(s)
Jacob van den Berg
Centrum Wiskunde & Informatica (CWI)
Rene Conijn
VU University Amsterdam
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12
Chayes L
, Nolin P. Large scale properties of the IIIC for 2D percolation.
Stoch Process Their Appl
2009. [DOI:
10.1016/j.spa.2008.04.002
]
[
Citation(s) in
RCA
: 2
]
[
Impact Index Per Article: 0.1
]
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[Indexed: 11/26/2022]
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13
Nolin P
. Near-critical percolation in two dimensions.
ELECTRON J PROBAB
2008. [DOI:
10.1214/ejp.v13-565
]
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Citation(s) in
RCA
: 55
]
[
Impact Index Per Article: 3.4
]
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[Indexed: 11/19/2022]
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Affiliation(s)
Pierre Nolin
Ecole Normale Supérieure and Université Paris-Sud
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