English

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 Zd\mathbb Z^d.

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