GOE statistics for Anderson models on antitrees and thin boxes in $\mathbb{Z}^3$ with deformed Laplacian

  title={GOE statistics for Anderson models on antitrees and thin boxes in \$\mathbb\{Z\}^3\$ with deformed Laplacian},
  author={Christian Sadel},
  journal={arXiv: Mathematical Physics},
  • Christian Sadel
  • Published 15 October 2017
  • Mathematics
  • arXiv: Mathematical Physics
Sequences of certain finite graphs, antitrees, are constructed along which the Anderson model shows GOE statistics, i.e. a re-scaled eigenvalue process converges to the ${\rm Sine}_1$ process. The Anderson model on the graph is a random matrix being the sum of the adjacency matrix and a random diagonal matrix with independent identically distributed entries along the diagonal. The strength of the randomness stays fixed, there is no re-scaling with matrix size. These considered random matrices… 
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