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The secular thickening of a self-gravitating stellar galactic disc isinvestigated using the dressed collisionless Fokker-Planck equation and theinhomogeneous multicomponent Balescu-Lenard equation. The thick WKB limits forthe diffusion fluxes are found using the epicyclic approximation, whileassuming that only radially tightly wound transient spirals are sustained bythe disc. This yields simple quadratures for the drift and diffusioncoefficients, providing a clear understanding of the positions of maximumvertical orbital diffusion within the disc, induced by fluctuations eitherexternal or due to the finite number of particles. These thick limits alsooffer a consistent derivation of a thick disc Toomre parameter, which is shownto be exponentially boosted by the ratio of the vertical to radial scaleheights. Dressed potential fluctuations within the disc statistically induce avertical bending of a subset of resonant orbits, triggering the correspondingincrease in vertical velocity dispersion. When applied to a tepid stabletapered disc perturbed by shot noise, these two frameworks reproducequalitatively the formation of ridges of resonant orbits towards largervertical actions, as found in direct numerical simulations, but overestimatesthe time-scale involved in their appearance. Swing amplification is likelyneeded to resolve this discrepancy, as demonstrated in the case of razor-thindiscs. Other sources of thickening are also investigated, such as fadingsequences of slowing bars, or the joint evolution of a population of giantmolecular clouds within the disc.

Resonant thickening of self-gravitating discs: imposed or self-induced orbital diffusion in the tightly wound limit