Full counting statistics of strongly non-ohmic transport through single molecules

We study analytically the full counting statistics of charge transport through single molecules, strongly coupled to a weakly damped vibrational mode. The specifics of transport in this regime-a hierarchical sequence of avalanches of transferred charges, interrupted by quiet periods-make the counting statistics strongly non-Gaussian. We support our findings for the counting statistics as well as for the frequency-dependent noise power by numerical simulations, finding excellent agreement.