论文标题
眼睛 - kramers定律，用于缓慢振荡双向扩散
An Eyring-Kramers law for slowly oscillating bistable diffusions
论文作者
论文摘要
我们考虑了二维随机微分方程，描述了在双孔电势中缓慢而定期强迫过度阻尼粒子的运动，受到弱添加噪声的影响。我们给出了眼环类型的尖锐渐近造型，以从一个潜在的井到另一个潜力的过渡时间。我们的结果涵盖了一系列强迫频率，这些频率相对于未强制系统的潜在井之间的最大过渡速率很大。分析的主要困难是强制系统是不可逆转的，因此不适用于获得可逆扩散的潜在理论的标准方法不适用。相反，我们使用Landim，Mariani和SEO的结果将潜在理论方法扩展到非可逆系统。
We consider two-dimensional stochastic differential equations, describing the motion of a slowly and periodically forced overdamped particle in a double-well potential, subjected to weak additive noise. We give sharp asymptotics of Eyring-Kramers type for the expected transition time from one potential well to the other one. Our results cover a range of forcing frequencies that are large with respect to the maximal transition rate between potential wells of the unforced system. The main difficulty of the analysis is that the forced system is non-reversible, so that standard methods from potential theory used to obtain Eyring-Kramers laws for reversible diffusions do not apply. Instead, we use results by Landim, Mariani and Seo that extend the potential-theoretic approach to non-reversible systems.
