奇异随机偏微分方程的精确Laplace渐近性：二维gPAM情形
Precise Laplace asymptotics for singular stochastic PDEs: The case of 2D gPAM
摘要：
我们实现了一个拉普拉斯方法的重整化解决方案的广义二维抛物安德森模型（gPAM）驱动的一个小的空间白噪声。我们的工作依赖于Hairer的正则性结构理论，它可以概括的经典思想Azencott和本Arous的道路空间以及阿伊达和稻滨和川比粗糙的道路空间的空间模型。我们的论点的技术基石是在噪声强度参数的解决方案的泰勒展开：我们证明其条款和其余部分的精确界限，并使用它们来估计渐近无关的条款，以任意顺序。虽然我们的大多数论点并不特定于gPAM，但我们也概述了如何适应这些论点。
英文摘要：
We implement a Laplace method for the renormalised solution to the generalised 2D Parabolic Anderson Model (gPAM) driven by a small spatial white noise. Our work rests upon Hairer's theory of regularity structures which allows to generalise classical ideas of Azencott and Ben Arous on path space as well as Aida and Inahama and Kawabi on rough path space to the space of models. The technical cornerstone of our argument is a Taylor expansion of the solution in the noise intensity parameter: We prove precise bounds for its terms and the remainder and use them to estimate asymptotically irrevelant terms to arbitrary order. While most of our arguments are not specific to gPAM, we also outline how to adapt those that are.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
