Answers are grounded in this paper and cite their sources.
We investigate the statistical behavior of the eigenvalues and diameter of random Cayley graphs of SL 2[Z/pZ] as the prime number p goes to infinity. We prove a density theorem for the number of exceptional eigenvalues of random Cayley graphs, i.e., the eigenvalues with absolute value bigger than the optimal spectral bound. Our numerical results suggest that random Cayley graphs of SL 2[Z/pZ] and the explicit LPS Ramanujan projective graphs of P1(Z/pZ) have optimal spectral gap and diameter as the prime number p goes to infinity.
No takes yet. Share an insight, caveat, or question.
Rivin et al. (2017) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: