Level Spacings for Sl(2; P) Level Spacings for Sl 2 (f P )
We investigate the eigenvalue spacing distributions for randomly generated 4-regular Cayley graphs on SL2(Fp) by numerically calculating their spectra. We present strong evidence that the distributions are Poisson and hence do not follow the Gaussian orthogonal ensemble. Among the Cayley graphs of SL2(Fp) we consider are the new expander graphs recently discovered by Y. Shalom. In addition, we use a Markov chain method to generate random 4-regular graphs, and observe that the average eigenvalue spacings are closely approximated by the Wigner surmise. LEVEL SPACINGS FOR SL2(Fp) JOHN D. LAFFERTY AND DANIEL N. ROCKMORE