Uniqueness of the infinite connected component for the vacant set of random interlacements on amenable transient graphs
Probability
2024-12-23 v2
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 .
Keywords
Cite
@article{arxiv.2304.09186,
title = {Uniqueness of the infinite connected component for the vacant set of random interlacements on amenable transient graphs},
author = {Yingxin Mu and Artem Sapozhnikov},
journal= {arXiv preprint arXiv:2304.09186},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2304.09153