耦合双稳态系统亚稳跃迁时间的一致估计
Uniform estimates for metastable transition times in a coupled bistable system
摘要：
我们考虑一个由布朗噪声驱动的耦合双稳态N粒子系统，强耦合对应于同步区。我们的目标是得到两个稳定状态之间的亚稳过渡时间的精确估计，无论是固定的N和在极限时，N趋于无穷大，误差估计均匀的N。这些估计是严格理解无限维系统亚稳态行为的重要一步，例如随机扰动的Ginzburg-Landau方程。我们的结果是基于潜在的亚稳性理论的方法。
英文摘要：
We consider a coupled bistable N-particle system driven by a Brownian noise, with a strong coupling corresponding to the synchronised regime. Our aim is to obtain sharp estimates on the metastable transition times between the two stable states, both for fixed N and in the limit when N tends to infinity, with error estimates uniform in N. These estimates are a main step towards a rigorous understanding of the metastable behavior of infinite dimensional systems, such as the stochastically perturbed Ginzburg-Landau equation. Our results are based on the potential theoretic approach to metastability.
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