Long time dynamics for interacting oscillators on graphs
Long time dynamics for interacting oscillators on graphs
复制标题
图表上相互作用振荡器的长时间动态
DOI：
10.1214/21-aap1680
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Fabio Coppini
中科院分区：
文献类型：
--
作者：
Fabio Coppini
分析了定义在图序列上的随机Kuramoto模型，重点讨论了平均场极限、图的连通性和长时间行为之间的关系。我们给出了一个关于图序列的显式确定性条件，使得对于任何有限时间和任何初始条件，即使依赖于网络，系统的经验测度也保持在与经典平均场极限相关的McKean-Vlasov方程的解附近。在这种情况下，我们研究了亚临界和超临界状态下的长时间行为：在这两个状态下，经验度量都保持在稳定稳定解的流形附近(可能退化)，直到大偏差现象开始之前，这些稳定稳定解的发散速度可以与系统大小的指数一样快。利用Grothendieck不等式推导出了图序列的条件，并将其表示为图序列在1到1$范数上的一个浓度.当系统的规模趋于无穷大时，假设每个站点的平均邻居数不同，则它被一大类随机的和确定的图所满足。
The stochastic Kuramoto model defined on a sequence of graphs is analyzed: the emphasis is posed on the relationship between the mean field limit, the connectivity of the underlying graph and the long time behavior. We give an explicit deterministic condition on the sequence of graphs such that, for any finite time and any initial condition, even dependent on the network, the empirical measure of the system stays close to the solution of the McKean-Vlasov equation associated to the classical mean field limit. Under this condition, we study the long time behavior in the subcritical and in the supercritical regime: in both regimes, the empirical measure stays close to the (possibly degenerate) manifold of stable stationary solutions, up to times which can diverge as fast as the exponential of the size of the system, before Large Deviation phenomena take over. The condition on the sequence of graphs is derived by means of Grothendieck's Inequality and expressed through a concentration in $\ell\_{\infty}\to \ell\_1$ norm. It is shown to be satisfied by a large class of graphs, random and deterministic, provided that the average number of neighbors per site diverges, as the size of the system tends to infinity.
影响因子：
1.1
作者：
Chiba, Hayato;Medvedev, Georgi S.
通讯作者：
Medvedev, Georgi S.
稀疏随机图上Kuramoto模型的连续统极限
影响因子：
1
作者：
Medvedev, Georgi S.
通讯作者：
Medvedev, Georgi S.