  The secular thickening of a discrete self-gravitating galactic disc is
investigated using the inhomogeneous multi-component Balescu-Lenard equation.
The thick WKB limit for the diffusion and drift coefficients is found using the
epicyclic approximation, while assuming that only radially tightly wound
transient spirals are sustained by the disc. This yields a simple double
quadrature for the drift and diffusion coefficients, providing a clear
understanding of the positions of maximum vertical orbital diffusion within the
disc induced by the effects of a finite number of particles. When applied to a
tepid stable tapered disc, the Balescu-Lenard formalism predicts the formation
of ridges of resonant orbits towards larger vertical actions, as found in
direct numerical simulations, but over-estimates the timescale involved in
their appearance. Swing amplication is likely needed to resolve this
discrepancy, as demonstrated in the case of razor-thin discs. The joint
evolution of a population of giant molecular clouds within the disc may
accelerate the secular disc's thickening induced by finite${-N}$ effects, but
the observed number of clouds in the Milky Way does not seem to be sufficient
to explain its thick disc.
