On the four-arm exponent for 2D percolation at criticality
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 , 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.
|M.E. Vares , R. Fernández (Roberto) , L.R. Fontes (Luiz Renato) , C.M. Newman|
|Progress in Probability|
|Organisation||Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands|
van den Berg, J, & Nolin, P. (2021). On the four-arm exponent for 2D percolation at criticality. In M.E Vares, R Fernández, L.R Fontes, & C.M Newman (Eds.), In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius (pp. 125–145). Springer Nature. doi:10.1007/978-3-030-60754-8_6