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arXiv · 1303.4908

The Large Connectivity Limit of the Anderson Model on Tree Graphs

Victor Bapst
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Abstract

We consider the Anderson localization problem on the infinite regular tree. Within the localized phase, we derive a rigorous lower bound on the free energy function recently introduced by Aizenman and Warzel. Using a finite volume regularization, we also derive an upper bound on this free energy function. This yields upper and lower bounds on the critical disorder such that all states at a given energy become localized. These bounds are particularly useful in the large connectivity limit where they match, confirming the early predictions of Abou-Chacra, Anderson and Thouless.

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Victor Bapst. 2014-09-09. The Large Connectivity Limit of the Anderson Model on Tree Graphs. https://doi.org/10.1063/1.4894055

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