Singular SPDEs: Approximation and Statistical Properties

正则性结构和次控制分布理论是奇异随机偏微分方程解的存在性、唯一性和正则性的重要理论。我们认为，现在时机已经成熟，可以进一步探索这些技术的全部力量：将它们扩展到导出解决方案的定性性质，特别是物理效应，如老化和不稳定性等。我们将对两个最突出和最有前途的方程，Kardar-Parisi-Zhang方程和抛物型安德森模型做这一点。通过结合我们在老化和免疫方面的专业知识（J. - D.D.和W.K.）和次受控分布/正则结构（N. P.）分别，我们处理了广泛的技术，这将使我们能够更好地了解这些方程。

The powerful and novel theories of regularity structures and paracontrolled distributions have so far been used mostly for deriving existence, uniqueness and regularity results for singular stochastic partial differential equations (SPDEs). We feel that the time is now mature for a further exploration of the full power of these techniques: to extend them for deriving qualitative properties of the solutions, in particular physical effects such as aging and intermittency and alike. We will do this for two of the most prominent and promising equations, the Kardar-Parisi-Zhang equation and the parabolic Anderson model. By combining our expertise in aging and intermittency (J.-D.D. and W.K.) and paracontrolled distributions / regularity structures (N.P.) respectively, we dispose of a wide range of techniques which will allow us to gain a much better understanding of these equations.