Percolation for the stable marriage of Poisson and Lebesgue

Marcelo Ventura Freire, Serguei Popov, Marina Vachkovskaia

Let $\Xi$ be the set of points (we call the elements of $\Xi$ centers) of Poisson process in ${\mathbb{R}}^d$, $d\ge 2$, with unit intensity. Consider the allocation of ${\mathbb{R}}^d$ to $\Xi$ which is s…