Level repulsion near integrability: a random matrix analogy

Using the analogy between the statistics of the levels of quantum Hamiltonians and the eigenvalues of random matrices the authors use (an appropriate choice of) the latter in order to study the transition region near integrability. They show that the nearest-neighbour spacing distribution is linear for small spacings while the inverse of its slope is proportional to the amplitude of the (integrability-destroying) perturbation.