1303.4908 (Victor Bapst)

The Large Connectivity Limit of the Anderson Model on Tree Graphs    [PDF]

Victor Bapst

We consider the Anderson localization problem on the infinite regular tree. Within the localized phase, we derive rigorous upper and lower bounds on the free energy function recently introduced by Aizenman and Warzel. With an additional but yet unproved regularity condition on this function, this leads to bounds on the critical disorder that induces localization. The latter are particularly useful in the limit of large connectivity where they match and confirm the early predictions of Abou-Chacra, Anderson and Thouless.

View original: http://arxiv.org/abs/1303.4908