  We explain in this paper how a meaningful irrelevant perturbation theory
around the infra-red (strong coupling) fixed point can be carried out for
integrable quantum impurity problems. This is illustrated in details for the
spin 1/2 Kondo model, where our approach gives rise to the complete low
temperature expansion of the resistivity, beyond the well known $T^2$ Fermi
liquid behaviour. We also consider the edge states tunneling problem, and
demonstrate by Keldysh techniques that the DC current satisfies an exact
duality between the UV and IR regimes. This corresponds physically to a duality
between the tunneling of Laughlin quasi particles and electrons, and, more
formally, to the existence of an exact instantons expansion. The duality is
deeply connected with integrability, and could not have been expected a priori.
