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

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