Percolation for the Finitary Random interlacements

Abstract

In this paper, we prove a phase transition in the connectivity of Finitary Random interlacements ${\mathcal{F}\mathcal{I}}^{u,T}$ in ${\mathbb{Z}}^d$, with respect to the average stopping time. For each $u>0$, with probability one ${\mathcal{F}\mathcal{I}}^{u,T}$ 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 ${\mathbb{Z}}^d$.

arXiv comment22 pages

References in corpus (5)

• Uniqueness and non-uniqueness in percolation theory
• On the internal distance in the interlacement set
• Connectivity properties of random interlacement and intersection of random walks
• On scaling limits and Brownian interlacements
• Eigenvalue vs perimeter in a shape theorem for self-interacting random walks

Cited by in corpus (2)

• On Chemical Distance and Local Uniqueness of a Sufficiently Supercritical Finitary Random Interlacement
• Some Rigorous Results on the Phase Transition of Finitary Random Interlacement