For two-dimensional percolation at criticality, we discuss the inequality α4 > 1 for the polychromatic four-arm exponent (and stronger versions, the strongest so far being ${\alpha }_{4}\ge 1+\frac{{\alpha }_{2}}{2}$ , where α2 denotes the two-arm exponent). We first briefly discuss five proofs (some of them implicit and not self-contained) from the literature. Then we observe that, by combining two of them, one gets a completely self-contained (and yet quite short) proof.
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doi.org/10.1007/978-3-030-60754-8_6
Progress in Probability
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

van den Berg, J, & Nolin, P. (2021). On the four-arm exponent for 2D percolation at criticality. In In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius (pp. 125–145). doi:10.1007/978-3-030-60754-8_6