Open Access
2023 Uniqueness of the infinite connected component for the vacant set of random interlacements on amenable transient graphs
Yingxin Mu, Artem Sapozhnikov
Author Affiliations +
Electron. Commun. Probab. 28: 1-9 (2023). DOI: 10.1214/23-ECP564

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 [10] to prove the uniqueness of the infinite connected component for the vacant set of random interlacements on Zd.

Funding Statement

The research of both authors has been supported by the DFG Priority Program 2265 “Random Geometric Systems” (Project number 443849139).

Citation

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Yingxin Mu. Artem Sapozhnikov. "Uniqueness of the infinite connected component for the vacant set of random interlacements on amenable transient graphs." Electron. Commun. Probab. 28 1 - 9, 2023. https://doi.org/10.1214/23-ECP564

Information

Received: 24 April 2023; Accepted: 4 November 2023; Published: 2023
First available in Project Euclid: 22 November 2023

arXiv: 2304.09186
Digital Object Identifier: 10.1214/23-ECP564

Subjects:
Primary: 60K35 , 82C41

Keywords: amenable graph , infinite connected component , percolation , Random interlacements , Random walk

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