The dimension of the Incipient Infinite Cluster

2014/05/29 by van Batenburg, Wouter Cames
#60K35 #82B43 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1405.7606

Abstract

We study the Incipient Infinite Cluster (IIC) of high-dimensional bond percolation on 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.

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