  This paper is devoted to the adaptation of the method developed in [4,3] to a
Fokker-Planck equation for fiber lay-down which has been studied in [1,5].
Exponential convergence towards a unique stationary state is proved in a norm
which is equivalent to a weighted $L^2$ norm. The method is based on a micro /
macro decomposition which is well adapted to the diffusion limit regime.
