  Thermal amplitudes with ultrasoft momenta, which are not accessible by
standard methods of perturbation theory, have recently attracted a lot of
interest. However, the comparison of external momenta with the ultrasoft scale
$g^2T\ln(1/g)$ is a too crude criterion, since amplitudes with hard external
momenta can also be non perturbative, if these momenta are close enough to the
light-cone. In this letter, I give a more refined criterion to decide if an
amplitude is non perturbative, that applies to all situations. In physical
terms, this condition states that non-perturbative effects appear if the
particles running in loops have to travel distances larger than their mean free
path.
