Statistics of Charge Fluctuations in Chaotic Cavities

We consider the zero frequency fluctuations of charge inside a mesoscopic conductor in the large capacitance limit. In analogy to current counting statistics we derive the characteristic function of charge fluctuations in terms of the scattering matrix of the conductor. Using random matrix theory we evaluate the characteristic function semi-analytically for chaotic cavities. Our result is universal in the sense that it describes not only the fluctuations of charge, but of any observable quantity inside the cavity. We discuss equilibrium and non-equilibrium fluctuations and extend our theory to the case of contacts with arbitrary transparency. Finally we investigate the suppression of fluctuations in the small capacitance limit due to charge screening.