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We evaluate the full statistics of the current via a Coulomb island that isstrongly coupled to the leads. This strong coupling weakens Coulombinteraction. We show that in this case the effects of the interaction can beincorporated into the renormalization of transmission eigenvalues of thescatterers that connect the island and the leads. We evaluate the Coulombblockade gap in the current-voltage characteristics, the value of the gap beingexponentially suppressed as compared to the classical charging energy of theisland.Comment: 4 pages, 3 figure

Full Current Statistics in the Regime of Weak Coulomb Interaction