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

Presented by: 
C Sadel Institute of Science and Technology (IST Austria)
Date: 
Thursday 9th April 2015 - 16:00 to 16:25
Venue: 
INI Seminar Room 1
Abstract: 
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons