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Percolative properties of Brownian interlacements and its vacant set. (English) Zbl 07268516
Summary: In this article, we investigate the percolative properties of Brownian interlacements, a model introduced by Sznitman (Bull Braz Math Soc New Ser 44(4):555-592, 2013), 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.
MSC:
60J65 Brownian motion
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
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