Maximal fluctuations around the Wulff shape for edge-isoperimetric sets in ${\mathbb{Z}}^d$: a sharp scaling law

Edoardo Mainini, Bernd Schmidt

We derive a sharp scaling law for deviations of edge-isoperimetric sets in the lattice ${\mathbb{Z}}^d$ from the limiting Wulff shape in arbitrary dimensions. As the number $n$ of ele…