## Electronic Communications in Probability

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

Artem Sapozhnikov

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 68, 775-780.

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

https://projecteuclid.org/euclid.ecp/1465262024

Digital Object Identifier
doi:10.1214/ECP.v16-1684

Mathematical Reviews number (MathSciNet)
MR2861441

Zentralblatt MATH identifier
1245.82059

Rights

#### Citation

Sapozhnikov, Artem. The incipient infinite cluster does not stochastically dominate the invasion percolation cluster in two dimensions. Electron. Commun. Probab. 16 (2011), paper no. 68, 775--780. doi:10.1214/ECP.v16-1684. https://projecteuclid.org/euclid.ecp/1465262024

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