基于SAW表示的安德森局域化化分数阶矩方法
Fractional Moment Methods for Anderson Localization with SAW Representation
摘要：
格林函数包含了许多关于物理系统的信息。在数学上，由Aizenman和Molchanov开发的分数矩方法（FMM）将格林函数和安德森模型中的电子输运联系起来。最近，人们已经发现，格林函数在图上可以表示使用自避免行走在图上，这使我们能够连接本地化属性的系统和图形的属性。我们讨论FMM的一般图上的自避免行走，唯一的一般条件是，该图有一个统一的边界上的顶点度。
英文摘要：
The Green's function contains much information about physical systems. Mathematically, the fractional moment method (FMM) developed by Aizenman and Molchanov connects the Green's function and the transport of electrons in the Anderson model. Recently, it has been discovered that the Green's function on a graph can be represented using self-avoiding walks on a graph, which allows us to connect localization properties in the system and graph properties. We discuss FMM in terms of the self-avoiding walks on a general graph, the only general condition being that the graph has a uniform bound on the vertex degree.
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