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 $2$.
Invasion percolation on regular trees
Critical Percolation and the Incipient Infinite Cluster on Galton-Watson Trees
The incipient infinite cluster does not stochastically dominate the invasion percolation cluster in two dimensions
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