Open Access
Translator Disclaimer
2011 The incipient infinite cluster does not stochastically dominate the invasion percolation cluster in two dimensions
Artem Sapozhnikov
Author Affiliations +
Electron. Commun. Probab. 16: 775-780 (2011). DOI: 10.1214/ECP.v16-1684

Abstract

This note is motivated by results of Angel, Goodman, den Hollander and Slade (2008) and Da, 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.

Citation

Download Citation

Artem Sapozhnikov. "The incipient infinite cluster does not stochastically dominate the invasion percolation cluster in two dimensions." Electron. Commun. Probab. 16 775 - 780, 2011. https://doi.org/10.1214/ECP.v16-1684

Information

Accepted: 30 November 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1245.82059
MathSciNet: MR2861441
Digital Object Identifier: 10.1214/ECP.v16-1684

Subjects:
Primary: 82C43
Secondary: 60K35, 82B27, 82B43

JOURNAL ARTICLE
6 PAGES


SHARE
Back to Top