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We study the current-voltage characteristic of a current biased array of normal tunnel junctions with small capacitance, 8/2C > kB T. It shows a Coulomb gap, which is found to scale with the number of junctions in series and to be independent of the number of junctions in parallel. The probability of single-electron tunnelling (SET) depends on the energy difference before and after the transition. This makes the Coulomb gap depend strongly on the size of the region probed by the electron in the tunnelling process. The amplitude of SET resonances is reduced compared to a single junction.

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