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

@article{Sadel2017GOESF,
title={GOE statistics for Anderson models on antitrees and thin boxes in \$\mathbb\{Z\}^3\$ with deformed Laplacian},
journal={arXiv: Mathematical Physics},
year={2017}
}
• 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…
1 Citations
• Mathematics
Annales Henri Poincaré
• 2020
We study the Laplacian on family preserving metric graphs. These are graphs that have a certain symmetry that, as we show, allows for a decomposition into a direct sum of one-dimensional operators

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