The dimension of the Incipient Infinite Cluster

preprint2014arXivOpen access

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 $2$ .

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The dimension of the Incipient Infinite Cluster

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