University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Anderson transition at 2D growth-rate for the Anderson model on antitrees with normalized edge weights

Anderson transition at 2D growth-rate for the Anderson model on antitrees with normalized edge weights

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Periodic and Ergodic Spectral Problems

An antitree is a discrete graph that is split into countably many shells $S_n$ consisting of finitely many vertices so that all vertices in $S_n$ are connected with all vertices in the adjacent shells $S_{n+1}$ and $S_{n-1}$. We normalize the edges between $S_n$ and $S_{n+1}$ with weights to have a bounded adjacency operator and add an iid random potential. We are interested in the case where the number of vertices $# S_n$ in the $n$-th shell grows like $n^a$. In a particular set of energies we obtain a transition of the spectral type from pure point to partly s.c. to a.c. spectrum at $a=1$ which corresponds to the growth-rate in 2 dimensions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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