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The variance of the incipient infinite cluster in two-dimensional percolation
Yu Zhang · 2016-03-21 · via math.PR updates on arXiv.org

Consider bond percolation on the square lattice. Let ${\cal C}$ be the incipient infinite cluster with the incipient measure $ν$. If a one-arm path exponent exists and equals $5/48$, it is well known that $E_ν|{\cal C}\cup [-n,n]^2| = n^{ 91/48+o(1)}$. In this paper, we focus on the variance of $|{\cal C}\cup [-n,n]^2|$ and show that $σ^2_ν(|{\cal C}\cup [-n,n]^2|)= n^{91/24+o(1)}$.

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