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

Zhenhao Cai, Xiao Han, Jiayan Ye, Yuan Zhang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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

Original languageEnglish
Pages (from-to)522-592
Number of pages71
JournalJournal of Theoretical Probability
Volume36
Issue number1
DOIs
StatePublished - 1 Mar 2023

Keywords

  • Chemical distance
  • Finitary random interlacements
  • Local uniqueness

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)
  • Statistics, Probability and Uncertainty

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