Does anyone know a straightforward proof of the Arctic Circle Theorem using the height function or any other method? I have tried to find one, but I only managed to dig up long papers.
2026-03-27 23:14:00.1774653240
Simple Proof of the Arctic Circle Theorem
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There is no straightforward proof. This paper by Pemantle & Wilson (Ex. 3.6) provides a good outline of the most direct approach. First one obtains a closed form multivariate GF for local statistics. This can be done in several ways, including a reasonably concise combinatorial approach. Then one uses the asymptotic analysis. This can also be done in several ways, none particularly obvious. See refs in the paper.