${\mathrm{ASL}}_n(\mathbb{Z})$ invariant random subsets of ${\mathbb{Z}}^n$

Mikołaj FrÄ czyk, Simon Machado

We classify measures on $\{0,1{\}}^{{\mathbb{Z}}^d}$, $d\ge 3$, the space of subsets of ${\mathbb{Z}}^d$, which are invariant under all affine special linear transformations. In other…