AI 中文总结
该研究否定了随机3-正则图全局同步的猜想，证明其以趋于1的概率不是全局同步的。
AI 中文摘要
我们研究随机 3-正则图上的齐次仓本模型。一个连通图 $G$ 是全局同步的，如果对于几乎所有的初始条件，梯度流收敛到完全同步状态，即所有相位一致。Bandeira [Oberwolfach Rep. 21 (2024) 1163-1226] 曾猜想随机 3-正则图 $G_{2n,3}$ 以高概率是全局同步的。我们以一种强方式否定了这个猜想：$G_{2n,3}$ 以趋于 1 的概率不是全局同步的。
英文摘要
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.
