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arXiv · 2304.09186

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

Yingxin Mu·Artem Sapozhnikov
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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 $\mathbb Z^d$.

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Yingxin Mu, Artem Sapozhnikov. 2024-12-20. Uniqueness of the infinite connected component for the vacant set of random interlacements on amenable transient graphs. https://doi.org/10.1214/23-ecp564

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