Counting statistics of tunneling current

The form of electron counting statistics of the tunneling current noise in a generic many-body interacting electron system is obtained and universal relations between its different moments are derived. A generalized fluctuation-dissipation theorem providing a relation between current and noise at arbitrary bias-to-temperature ratio eV∕k_BT is established in the tunneling Hamiltonian approximation. The third correlator of current fluctuations S₃ (the skewness of the charge counting distribution) has a universal Schottky-type relation with the current and quasiparticle charge that holds in a wide bias voltage range, both at large and small eV∕k_BT . The insensitivity of S₃ to the Nyquist-Schottky crossover represents an advantage compared to the Schottky formula for the noise power. We discuss the possibility of using the correlator S₃ for detecting quasiparticle charge at high temperatures.