Percolative Properties of Brownian Interlacements and Its Vacant Set

Xinyi Li ()
Additional contact information
Xinyi Li: Peking University

Journal of Theoretical Probability, 2020, vol. 33, issue 4, 1855-1893

Abstract: Abstract 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, $$d\ge 3$$ d ≥ 3 , can be connected via no more than $$\lceil (d-4)/2 \rceil $$ ⌈ ( d - 4 ) / 2 ⌉ intermediate sausages almost surely; while the vacant set undergoes a non-trivial percolation phase transition when the level parameter varies.

Keywords: Brownian interlacements; Random interlacements; Wiener sausage; Percolation; 60J65; 60K35; 82B43 (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-019-00944-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:33:y:2020:i:4:d:10.1007_s10959-019-00944-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-019-00944-7

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().