The dimension of the incipient infinite cluster. (English) Zbl 1327.60182

Summary: We study the incipient infinite cluster (IIC) of high-dimensional bond percolation on \(\mathbb{Z}^d\). We prove that the mass dimension of the IIC almost surely equals 4 and the volume growth exponent of the IIC almost surely equals 2.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
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