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We analyze the full counting statistics (FCS) of a single-site quantum dotcoupled to a local Holstein phonon for arbitrary transmission and weakelectron-phonon coupling. We identify explicitly the contributions due toquasielastic and inelastic transport processes in the cumulant generatingfunction and discuss their influence on the transport properties of the dot. Wefind that in the low-energy sector, the inelastic term causes a sign change inthe shot noise correction at certain universal values of the transmission.Furthermore, we show that when the correction to the current due to inelasticprocesses vanishes, all odd order cumulants vanish as well.

Charge transfer statistics of a molecular quantum dot with a vibrational degree of freedom