We consider a coupled bistable $N$-particle system on $mathbb{R}^N$ 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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机译：我们考虑由布朗噪声驱动的$ mathbb {R} ^ N $上的耦合双稳态$ N $粒子系统，其强耦合对应于同步状态。我们的目标是对两个稳定状态之间的亚稳态跃迁时间进行精确估计，无论是对于固定的N $美元，还是在N $趋于无穷大的极限内，误差估计均在$ N $内。这些估计是朝着严格理解无限维系统（例如随机扰动的Ginzburg-Landau方程）的亚稳行为迈出的重要一步。我们的结果基于亚稳态的潜在理论方法。
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