Intermittency phenomena in random media

本文研究了空间分布随机系统的两种模型——抛物型Anderson模型（PAM）和Mullins-Sekerka进化（MSB）对Ostwald成熟的影响。间断性表现为系统的高度不规则演化，由越来越稀疏分布的极端行为区域的出现所决定。我们开发了新的光谱方法来研究PAM在极端区域解的几何形状，以及处理高度不规则随机环境中随机游动的亚扩散率和老化。对于PAM，我们还研究了跳跃输运等精细化的动态问题，并处理了时变和漂移随机电位的间歇性问题。对于MSE，我们提出在整个空间上构建一个版本的模型，并特别考虑随机位置粒子的碰撞、筛选效应和系统的渐近自相似。

We investigate the effect of intermittency in two models of spatially distributed random systems, the parabolic Anderson model (PAM) and the Mullins-Sekerka evolution (MSB) for Ostwald ripening. Intermittency manifests itself in a highly irregular evolution of the system determined by the appearance of more and more sparsely distributed regions of extreme behaviour. We develop new spectral methods to study the geometry of the solution to the PAM in extreme regions and to treat subdiffusivity and aging for random walks in highly irregular random environment. For the PAM, we also study refined dynamic questions like the hopping transport and deal with intermittency for time-dependent and drifted random potentials. For the MSE, we propose to construct a version of the model on the entire space and study it with particular consideration of the collisions of the randomly located particles, the screening effect, and asymptotic self-similarity of the system.