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DAMUT Colloquium archive

2026

  • Date: 04 March 2026 in Room RA-2501
    Speaker: Dr. Martijn Gösgens (MDS/MOR-SOR)
    Title: Geometry hinders the formation of consensus in asynchronous majority dynamics
    Abstract: We investigate a model of opinion dynamics where vertices asynchronously announce opinions based on their private opinion and on the previously announced opinions of their neighbors. Our focus is on understanding how the structure of the underlying graph influences the likelihood of reaching consensus on the true opinion. Previous work proved that for sufficiently sparse, connected expander graphs, this process terminates in consensus on the true opinion with high probability. In this work, we show that when the underlying graph has geometric structure, the process is likely to terminate in disconsensus. Specifically, we prove that for a one-dimensional Random Geometric Graph (RGG) of n vertices with expected degree o(√n), the process ends in disconsensus with high probability. Numerical experiments indicate that this phenomenon persists in higher-dimensional RGGs. Instead of a global consensus, we observe that the geometry leads to local consensuses.

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