  In this article we investigate the percolative properties of Brownian
interlacements, a model introduced by Alain-Sol Sznitman in arXiv:1209.4531,
and show that: the interlacement set is "well-connected", i.e., any two
"sausages" in $d$-dimensional Brownian interlacements, $d\geq 3$, can be
connected via no more than $\lceil (d-4)/2 \rceil$ intermediate sausages almost
surely; while the vacant set undergoes a non-trivial percolation phase
transition when the level parameter varies.
