Galina Sidorenko, Johan Thunberg · 2026 · arXiv
DOI: 10.48550/arXiv.2610.28341 · open-access PDF
Kami mempelajari konsensus waktu diskrit pada sfer unit Euclidean, di mana kombinasi yang dipertaruhkan dari negara-negara tetangga diatur menjadi panjang unit. Untuk berat simetris pada grafik yang terhubung tanpa arah dan dimensi lingkungan $d\ge3$, hasil sebelumnya menetapkan ketidakstabilan titik tetap non-konsensus di bawah kondisi berat yang tepat. Untuk grafik terarah pada lingkaran unit, hasil sebelumnya menunjukkan bahwa titik tetap selain konsensus dan konfigurasi antipodal terjadi hanya untuk seperangkat ukuran nol berat.
Machine translation (Meta M2M100); the English original follows.
We study discrete-time consensus on the Euclidean unit sphere, where weighted combinations of neighboring states are normalized to unit length. For symmetric weights on connected undirected graphs and ambient dimension $d\ge3$, earlier results establish instability of non-consensus fixed points under suitable weight conditions. For directed graphs on the unit circle, earlier results show that fixed points other than consensus and antipodal configurations occur only for a measure-zero set of weights. We show that these conclusions do not extend directly to general strongly connected directed gr
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