Percolation for the Finitary Random interlacements
Abstract
In this paper, we prove a phase transition in the connectivity of Finitary Random interlacements $\mathcal{FI}^{u,T}$ in $\mathbb{Z}^d$, with respect to the average stopping time. For each $u>0$, with probability one $\mathcal{FI}^{u,T}$ has no infinite connected component for all sufficiently small $T>0$, and a unique infinite connected component for all sufficiently large $T<\infty$. This answers a question of Bowen in the special case of $\mathbb{Z}^d$.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2019
- DOI:
- 10.48550/arXiv.1908.01954
- arXiv:
- arXiv:1908.01954
- Bibcode:
- 2019arXiv190801954P
- Keywords:
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- Mathematics - Probability
- E-Print:
- 22 pages