Consider critical Bernoulli bond percolation on $\mathbb{Z}^2$. We show that the two arm exponent is strictly larger than twice the one arm exponent. This answers a question of Schramm and Steif (2010), and shows that their proof of the existence of exceptional times on the triangular lattice also applies to the square lattice. We use an interpolation formula via noise to obtain asymptotic correlation of crossings and apply this at each scale to obtain the strict inequality of arm exponents. This talk is based on joint work with Vincent Tassion.

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Last updated: 19 Jul 2024