Asymptotic singular windings of ergodic diffusions

Let M be a complete connected oriented Riemannian manifold of dimension n [greater-or-equal, slanted] 3; let X be a symmetrizable ergodic diffusion on M; let y be an oriented compact submanifold of M, of codimension 2; let Nt be the linking number between y and X [0, t]; then t-1 Nt converges in law towards a Cauchy variable, whose parameter is calculated; this result is extended mainly to the stochastic bridge, to the finite marginals of the processes (Xrt, t-1 Nrt), and to the integral along X[0, t] of [omega] [epsilon] H1 (M/y)/H1 (M).