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The incipient infinite cluster does not stochastically dominate the invasion percolation cluster in two dimensions

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1.	Title	Title of document	The incipient infinite cluster does not stochastically dominate the invasion percolation cluster in two dimensions
2.	Creator	Author's name, affiliation, country	Artem Sapozhnikov; ETH Zürich; Switzerland
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Invasion percolation, incipient infinite cluster, critical percolation, near-critical percolation, correlation length, stochastic domination.
3.	Subject	Subject classification	82C43; 60K35; 82B27; 82B43.
4.	Description	Abstract	This note is motivated by results of Angel, Goodman, den Hollander and Slade (2008) and Damron, Sapozhnikov and Vagvolgyi (2009) about global relations between the invasion percolation cluster (IPC) and the incipient infinite cluster (IIC) on regular trees and on two dimensional lattices, respectively. Namely, that the laws of the two objects are mutually singular, and, in the case of regular trees, that the IIC stochastically dominates the IPC. We prove that on two dimensional lattices, the IIC does not stochastically dominate the IPC. This is the first example showing that the relation between the IIC and IPC is significantly different on trees and in two dimensions.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2011-11-30
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1684
10.	Identifier	Digital Object Identifier	10.1214/ECP.v16-1684
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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