It has been conjectured that the eigenvalues of the adjacency matrix of a large box in $Z^d, d>=3$, perturbed by the right amount of randomness, behave like the eigenvalues of a random matrix. I will discuss this and related conjectures, explain what happens in one dimension, and present a very special provable case of long boxes. Based on joint work with E. Kritchevski and B. Valko.