Title
"On the large connectivity limit of the Anderson model on tree graphs"
Victor Bapst (Ecole Normale Supérieure, Paris)
Abstract
The Anderson model on a regular tree is a convenient model to study the spectrum of operators combining a hopping term and a random potential. In particular, one expects that upon varying the strength of the random potential, the spectral type of the operator varies, with a mobility edge separating localized states from extended one.
I present a result on the asymptotic of the mobility edge for this model in the limit where the connectivity of the tree goes to infinity. Using the criterion for localization/delocalization recently obtained by Aizenman and Warzel, I show how one can obtain bounds on the value of the mobility edge, that asymptotically match.
