The Parabolic Anderson Model
The Parabolic Anderson Model
复制标题
抛物线安德森模型
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
W. Koenig
中科院分区：
文献类型：
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作者：
J. Gaertner;W. Koenig
本文综述了抛物型安德森模型的间歇性，它是格点上具有随机势的热方程的柯西问题。我们首先介绍该模型，并对溶液的长期行为给出启发式解释，无论是在与时间无关的势的退火和淬火设置中。因此，我们认为潜在的文献中研究的例子。在特别重要的i.i.d.情况下。势的双指数尾，我们制定了详细的渐近结果。此外，我们解释说，在温和的正则性假设下，只有四个不同的普遍性类的渐近行为。最后，我们研究了由泊松随机游动场产生的时空齐次催化势的矩李雅普诺夫指数。
This is a survey on the intermittent behavior of the parabolic Anderson model, which is the Cauchy problem for the heat equation with random potential on the lattice ℤd. We first introduce the model and give heuristic explanations of the long-time behavior of the solution, both in the annealed and the quenched setting for time-independent potentials. We thereby consider examples of potentials studied in the literature. In the particularly important case of an i.i.d. potential with double-exponential tails we formulate the asymptotic results in detail. Furthermore, we explain that, under mild regularity assumptions, there are only four different universality classes of asymptotic behaviors. Finally, we study the moment Lyapunov exponents for space-time homogeneous catalytic potentials generated by a Poisson field of random walks.