Counting statistics in multistable systems

Using a microscopic model for stochastic transport through a single quantum dot that is modified by the Coulomb interaction of environmental (weakly coupled) quantum dots, we derive generic properties of the full counting statistics for multistable Markovian transport systems. We study the temporal crossover from multi-modal to broad unimodal distributions depending on the initial mixture, the long-term asymptotics and the divergence of the cumulants in the limit of a large number of transport branches. Our findings demonstrate that the counting statistics of a single resonant level may be used to probe background charge configurations.