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The Green's function contains much information about physical systems.Mathematically, the fractional moment method (FMM) developed by Aizenman andMolchanov connects the Green's function and the transport of electrons in theAnderson model. Recently, it has been discovered that the Green's function on agraph can be represented using self-avoiding walks on a graph, which allows usto connect localization properties in the system and graph properties. Wediscuss FMM in terms of the self-avoiding walks on a general graph, the onlygeneral condition being that the graph has a uniform bound on the vertexdegree.

Fractional Moment Methods for Anderson Localization with SAW Representation