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2015 The dimension of the incipient infinite cluster
Wouter Cames van Batenburg
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Electron. Commun. Probab. 20: 1-10 (2015). DOI: 10.1214/ECP.v20-3570

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 $2$.

Citation

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Wouter Cames van Batenburg. "The dimension of the incipient infinite cluster." Electron. Commun. Probab. 20 1 - 10, 2015. https://doi.org/10.1214/ECP.v20-3570

Information

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

zbMATH: 1327.60182
MathSciNet: MR3342167
Digital Object Identifier: 10.1214/ECP.v20-3570

Subjects:
Primary: AMS MSC 2010

Keywords: 60K35, 82B43

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