  The production of o(1/g^2) particles in a weakly-coupled theory is believed
to be non-perturbatively suppressed. I comment on the prospects of (a)
establishing this rigorously, and (b) estimating the effect to exponential
accuracy semiclassically, by discussing two closely-related problems: the
large-order behaviour of few-point Green functions, and induced excitation in
quantum mechanics. Induced tunneling in the latter case is exponentially
enhanced for frequencies of the order of the barrier height.
