On Chemical Distance and Local Uniqueness of a Sufficiently Supercritical Finitary Random Interlacements

Zhenhao Cai (), Xiao Han (), Jiayan Ye () and Yuan Zhang ()
Additional contact information
Zhenhao Cai: Peking University
Xiao Han: Peking University
Jiayan Ye: Ben Gurion University of the Negev
Yuan Zhang: Peking University

Journal of Theoretical Probability, 2023, vol. 36, issue 1, 522-592

Abstract: Abstract In this paper, we study geometric properties of the unique infinite cluster $$\Gamma ^{u,T}$$ Γ u , T in a sufficiently supercritical finitary random interlacements $$\mathcal {FI}^{u,T}$$ FI u , T in $${\mathbb {Z}}^d, \ d\ge 3$$ Z d , d ≥ 3 . We prove that the chemical distance in $$\Gamma ^{u,T}$$ Γ u , T is, with stretched exponentially high probability, of the same order as the Euclidean distance in $${\mathbb {Z}}^d$$ Z d . This also implies a shape theorem parallel to those for percolation and regular random interlacements. We also prove local uniqueness of $$\mathcal {FI}^{u,T}$$ FI u , T , which says that any two large clusters in $$\mathcal {FI}^{u,T}$$ FI u , T “close to each other" will be connected within the same order of their diameters except a stretched exponentially small probability.

Keywords: Finitary random interlacements; Chemical distance; Local uniqueness; 60K35; 60G50 (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-022-01182-0 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:36:y:2023:i:1:d:10.1007_s10959-022-01182-0

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

DOI: 10.1007/s10959-022-01182-0

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 ().