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2022 Dynamical noise sensitivity for the voter model
Gideon Amir, Omer Angel, Rangel Baldasso, Ron Peretz
Author Affiliations +
Electron. Commun. Probab. 27: 1-7 (2022). DOI: 10.1214/22-ECP483

Abstract

We study noise sensitivity of the consensus opinion of the voter model on finite graphs, with respect to noise affecting the initial opinions and noise affecting the dynamics. We prove that the final opinion is stable with respect to small perturbations of the initial configuration, and is sensitive to perturbations of the dynamics governing the evolution of the process. Our proofs rely on the duality relationship between the voter model and coalescing random walks, and on a precise description of this evolution when we have coupled dynamics.

Funding Statement

GA counted on the support of the Israel Science Foundation through Grant 957/20. OA is supported in part by NSERC. RB thanks the Mathematical Institute of Leiden University for support. RP was supported in part by the Israel Science Foundation Grant 2566/20.

Acknowledgments

We thank Itai Benjamini for raising the questions studied in this paper.

Citation

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Gideon Amir. Omer Angel. Rangel Baldasso. Ron Peretz. "Dynamical noise sensitivity for the voter model." Electron. Commun. Probab. 27 1 - 7, 2022. https://doi.org/10.1214/22-ECP483

Information

Received: 1 December 2021; Accepted: 14 August 2022; Published: 2022
First available in Project Euclid: 23 September 2022

arXiv: 2111.12354
Digital Object Identifier: 10.1214/22-ECP483

Subjects:
Primary: 60J27 , 60K35 , 82C22

Keywords: consensus opinion , Noise sensitivity , Noise stability , voter model

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