Decoupling inequalities in loop percolation

2020. 02. 20. 16:15
Caio Alves (Leipzig)

In this talk we are going to talk about a percolation process which arises from a Poissonian ensemble of simple random walk loops in Z^d, for three dimensions or more. This is a dependent percolation process, states of vertices have correlations which decay polynomially in the distance between said vertices. Furthermore, strong decoupling inequalities such as those available for the gaussian free field or the random interlacements processes are believed to be false in the loop percolation case. We present a weaker inequality, which holds for the loop ensemble, and nevertheless allows one to prove several results for this model which were previously out of reach.