  We derive expressions for the probability distribution of the ratio of two
consecutive level spacings for the classical ensembles of random matrices. This
ratio distribution was recently introduced to study spectral properties of
many-body problems, as, contrary to the standard level spacing distributions,
it does not depend on the local density of states. Our Wigner-like surmises are
shown to be very accurate when compared to numerics and exact calculations in
the large matrix size limit. Quantitative improvements are found through a
polynomial expansion. Examples from a quantum many-body lattice model and from
zeros of the Riemann zeta function are presented.
