The parabolic Anderson model with heavy-tailed potential
The parabolic Anderson model with heavy-tailed potential
复制标题
具有重尾潜力的抛物线安德森模型
DOI：
10.4171/072-1/4
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Peter Mörters
中科院分区：
文献类型：
--
作者：
Peter Mörters
抛物型安德森模型是具有随机位势的热方程的柯西问题。它提供了一个案例研究的影响，一个随机的，或不规则的，环境可以对扩散过程。在本调查的主要重点是现象，是由于一个高度不规则的潜力，我们的模型由一个空间独立的，同分布的随机场与重尾。在我们讨论的影响是随机波动的增长，总质量，本地化在弱和几乎肯定的意义上，和老化。2010年数学学科分类。小学60K37中学82C44.
The parabolic Anderson model is the Cauchy problem for the heat equation with random potential. It offers a case study for the effects that a random, or irregular, environment can have on a diffusion process. The main focus in the present survey is on phenomena that are due to a highly irregular potential, which we model by a spatially independent, identically distributed random field with heavy tails. Among the effects we discuss are random fluctuations in the growth of the total mass, localisation in the weak and almost sure sense, and ageing. 2010 Mathematics Subject Classification. Primary 60K37 Secondary 82C44.