Exact Small Time Equivalent for the density of the Circular Langevin Diffusion

A small time equivalent of the density is obtained for the circular analogue of the Langevin diffusion, which is strictly hypoelliptic (and non-Gaussian), hence of a different nature as the known sub-Riemannian case. The singular case, analogous to the case of conjugate points (the cut-locus problem) in the sub-Riemannian framework, is totally handled too, though much more difficultly.