  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 giving GOE statistics can also be viewed
as random Schr\"odinger operators $\mathcal{P}\Delta+\mathcal{V}$ on thin
finite boxes in $\mathbb{Z}^3$ where the Laplacian $\Delta$ is deformed by a
projection $\mathcal{P}$ commuting with $\Delta$.
