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arXiv · 2610.09135

Random $3$-regular graphs are not globally synchronizing

Ciro Carvallo·Pablo Groisman·Dieter Mitsche
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Abstract

We study the homogeneous Kuramoto model on random 3-regular graphs. A connected graph $G$ is globally synchronizing if, for almost every initial condition, the gradient flow converges to a fully synchronized state, in which all phases coincide. It has been conjectured by Bandeira [Oberwolfach Rep. 21 (2024) 1163-1226] that a random 3-regular graph $G_{2n,3}$ is globally synchronizing with high probability. We disprove this conjecture in a strong way: $G_{2n,3}$ is not globally synchronizing with probability tending to 1.

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Ciro Carvallo, Pablo Groisman, Dieter Mitsche. 2026-10-10. Random $3$-regular graphs are not globally synchronizing. https://arxiv.org/abs/2610.09135

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