Fumika Suzuki
Published 2017-04-20Version 1
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.
Comments: This is an author-created, un-copyedited version of an article published in Journal of Physics A. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8113/46/12/125008
Journal: J. Phys. A: Math. Theor. 46 125008 (2013)
Fractional Moment Methods for Anderson Localization in the Continuum
Anderson localization on a simplex
$SLE(κ,ρ)$ processes, hiding exponents and self-avoiding walks in a wedge
![QR code for arXiv:1704.06003 [math-ph]](http://oss.arxitics.com/images/favicon.svg)