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

   
@article{ECP1684,
	author = {Artem Sapozhnikov},
	title = {The incipient infinite cluster does not stochastically dominate the invasion percolation cluster in two dimensions},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {16},
	year = {2011},
	keywords = {Invasion percolation, incipient infinite cluster, critical percolation, near-critical percolation,   correlation length, stochastic domination.},
	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.},
	pages = {no. 68, 775-780},
	issn = {1083-589X},
	doi = {10.1214/ECP.v16-1684},    
        url = {http://ecp.ejpecp.org/article/view/1684}}