Local percolative properties of the vacant set of random interlacements with small intensity

@inproceedings{Drewitz2013LocalPP,
title={Local percolative properties of the vacant set of random interlacements with small intensity},
author={Alexander Drewitz and Bal{\'a}zs R{\'a}th and Art{\"e}m Sapozhnikov},
year={2013}
}

Random interlacements at level u is a one parameter family of connected random subsets of Z, d ≥ 3 [11]. Its complement, the vacant set at level u, exhibits a non-trivial percolation phase transition in u [11, 10], and the infinite connected component, when it exists, is almost surely unique [13]. In this paper we study local percolative properties of the vacant set of random interlacements at level u for all dimensions d ≥ 3 and small intensity parameter u > 0. We give a stretched exponential… CONTINUE READING