## Electronic Communications in Probability

### The dimension of the incipient infinite cluster

Wouter Cames van Batenburg

#### Abstract

We study the Incipient Infinite Cluster (IIC) of high-dimensional bond percolation on $\mathbb{Z}^d$. We prove that the mass dimension of IIC almost surely equals $4$ and the volume growth exponent of IIC almost surely equals $2$.

#### Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 33, 10 pp.

Dates
Accepted: 9 April 2015
First available in Project Euclid: 7 June 2016

https://projecteuclid.org/euclid.ecp/1465320960

Digital Object Identifier
doi:10.1214/ECP.v20-3570

Mathematical Reviews number (MathSciNet)
MR3342167

Zentralblatt MATH identifier
1327.60182

Subjects
Primary: AMS MSC 2010

Keywords
60K35 82B43

Rights

#### Citation

Cames van Batenburg, Wouter. The dimension of the incipient infinite cluster. Electron. Commun. Probab. 20 (2015), paper no. 33, 10 pp. doi:10.1214/ECP.v20-3570. https://projecteuclid.org/euclid.ecp/1465320960

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