Percolative properties of Brownian interlacements and its vacant set

Abstract

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, $d\ge 3$, 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.

33 pages

References in corpus (4)

• Soft local times and decoupling of random interlacements
• On the uniqueness of the infinite cluster of the vacant set of random interlacements
• On scaling limits and Brownian interlacements
• A short proof of the phase transition for the vacant set of random interlacements

Cited by in corpus (1)

• The Component Graph of the Uniform Spanning Forest: Transitions in Dimensions $9,10,11,\dots$