Decoupling inequalities and supercritical percolation for the vacant set of random walk loop soup

Caio Alves, Artem Sapozhnikov

It has been recently understood (arXiv:1212.2885, arXiv:1310.4764, arXiv:1410.0605) that for a general class of percolation models on ${\mathbb{Z}}^d$ satisfying suitable decoupling…