论文标题
Métastabilitéd'Edp随机物与弗雷德尔姆
Métastabilité d'EDP stochastiques et déterminants de Fredholm
论文作者
论文摘要
当热力学系统（例如超冷水（低于冰冻温度））降落在相变的“错误”一侧，并且在与其平衡状态不同的状态下，将会出现亚稳定性。存在许多描述这种现象的数学模型，包括具有随机动力学的晶格模型。在本文中，我们将对抛物线随机部分微分方程（SPDE）中的亚稳定性感兴趣。这些方程中的一些是不适合的，只有由于所谓的奇异SPDES理论的最新进展，只有通过重态化程序才能构建解决方案。这些系统中的亚稳定性的研究揭示了与频谱决定因素理论的意外联系，包括弗雷德尔姆和卡尔曼 - 弗雷德霍尔姆决定因素。
Metastability appears when a thermodynamic system, such as supercooled water (which is liquid below freezing temperature), lands on the "wrong" side of a phase transition, and remains for a very long time in a state different from its equilibrium state. There exist numerous mathematical models describing this phenomenon, including lattice models with stochastic dynamics. In this text, we will be interested in metastability in parabolic stochastic partial differential equations (SPDEs). Some of these equations are ill-posed, and only thanks to very recent progress in the theory of so-called singular SPDEs does one how to construct solutions, via a renormalisation procedure. The study of metastability in these systems reveals unexpected links with the theory of spectral determinants, including Fredholm and Carleman--Fredholm determinants.
