Kuramoto同步模型中涨落SPDE的大时间渐近性
Large time asymptotics for the fluctuation SPDE in the Kuramoto synchronization model
摘要：
研究了仓本同步模型中涨落SPDE的长时间渐近性。我们建立了大时间的线性行为和弱无序的淬火极限涨落的粒子周围的McKean-Vlasov极限的经验测量。这是通过对底层无界演化算子的谱分析，利用自伴算子和解析半群的扰动参数来实现的。我们特别指出，若尔当分解的发展算子，这是关键点，以表明无序仓本模型的波动是不自平均。
英文摘要：
We investigate the long-time asymptotics of the fluctuation SPDE in the Kuramoto synchronization model. We establish the linear behavior for large time and weak disorder of the quenched limit fluctuations of the empirical measure of the particles around its McKean-Vlasov limit. This is carried out through a spectral analysis of the underlying unbounded evolution operator, using arguments of perturbation of self-adjoint operators and analytic semigroups. We state in particular a Jordan decomposition of the evolution operator which is the key point in order to show that the fluctuations of the disordered Kuramoto model are not self-averaging.
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