# Excess deviations for points disconnected by random interlacements

Alain-Sol Sznitman

Alain-Sol Sznitman

**1/9/20**Published in : arXiv:2009.00601

We consider random interlacements on

\mathbb{Z}^d |

,

d \ge 3 |

, when their vacant set is in a strongly percolative regime. Given a large box centered at the origin, we establish an asymptotic upper bound on the exponential rate of decay of the probability that the box contains an excessive fraction ν of points that are disconnected by random interlacements from the boundary of a concentric box of double size. As an application we show that when ν is not too large, this asymptotic upper bound matches the asymptotic lower bound derived in a previous work of the author, and the exponential rate of decay is governed by a certain variational problem in the continuum which involves the percolation function of the vacant set of random interlacements.