Arithmetic oscillations of the chemical distance in long-range percolation on ${\mathbb{Z}}^d$

Marek Biskup, Andrew Krieger

We consider a long-range percolation graph on ${\mathbb{Z}}^d$ where, in addition to the nearest-neighbor edges of ${\mathbb{Z}}^d$, distinct $x,y\in {\mathbb{Z}}^d$ are connected by an edge…