Uniqueness of the infinite connected component for the vacant set of random interlacements on amenable transient graphs

Abstract

We prove the uniqueness of the infinite connected component for the vacant set of random interlacements on general vertex-transitive amenable transient graphs. Our approach is based on connectedness of random interlacements and differs from the one used by Teixera arXiv:0805.4106 to prove the uniqueness of the infinite connected component for the vacant set of random interlacements on ${\mathbb{Z}}^d$.

arXiv admin note: text overlap with arXiv:2304.09153

References in corpus (2)

• On the uniqueness of the infinite cluster of the vacant set of random interlacements
• Equality of critical parameters for percolation of Gaussian free field level-sets

Cited by in corpus (1)

• On questions of uniqueness for the vacant set of Wiener sausages and Brownian interlacements