# 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}, author={Christian Sadel}, journal={arXiv: Mathematical Physics}, year={2017} }

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…

## One Citation

### On the Decomposition of the Laplacian on Metric Graphs

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- 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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