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 language | English |
---|---|
Pages (from-to) | 522-592 |
Number of pages | 71 |
Journal | Journal of Theoretical Probability |
Volume | 36 |
Issue number | 1 |
DOIs | |
State | Published - 1 Mar 2023 |
Keywords
- Chemical distance
- Finitary random interlacements
- Local uniqueness
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty