论文标题
吉布斯不变的量度I：眼环公式的非可逆亚稳态扩散
Non-reversible Metastable Diffusions with Gibbs Invariant Measure I: Eyring-Kramers Formula
论文作者
论文摘要
在本文中，我们证明了具有吉布斯不变度度量的非可逆亚稳态扩散过程的眼环式公式。我们的结果表明，与[Bovier，Eckhoff，Gayrard和Klein，J。Eur中考虑的可逆过程相比，非可逆过程在当地最小值的邻居之间表现出更快的亚稳态过渡。数学。 Soc。 6：399-424，2004]。因此，通过为模型增加非可逆性，我们确实可以加速亚稳态过渡。我们的证明是基于通过准确估计亚稳态山谷之间的容量的潜在理论方法。我们通过开发一种新的方法来计算能力的尖锐渐近物，而无需依赖诸如dirichlet原理或汤姆森原理等变化原理的情况下进行估计。
In this article, we prove the Eyring-Kramers formula for non-reversible metastable diffusion processes that have a Gibbs invariant measure. Our result indicates that non-reversible processes exhibit faster metastable transitions between neighborhoods of local minima, compared to the reversible process considered in [Bovier, Eckhoff, Gayrard, and Klein, J. Eur. Math. Soc. 6: 399-424, 2004]. Therefore, by adding non-reversibility to the model, we can indeed accelerate the metastable transition. Our proof is based on the potential theoretic approach to metastability through accurate estimation of the capacity between metastable valleys. We carry out this estimation by developing a novel method to compute the sharp asymptotics of the capacity without relying on variational principles such as the Dirichlet principle or the Thomson principle.
