It has long been recognized that for the GUE, the asymptotic size of the gap at 0, the location of the smallest positive eigenvalue, the (local) empirical measure of spacings between eigenvalues in the bulk, and similar quantities are all related. The “folklore” proof uses combinatorics and inclusion-exclusion relations, but is not completely transparent. I will describe an alternative approach, based on the fact that the eigenvalues process is determinantal with a limiting kernel, the sine kernel, that is shift invariant.