2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/25614We 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.4+ pages, 2 figures; minor changes, version published in Phys. Rev. LettMesoscale and Nanoscale Physicstext