We have used numerical modeling and a semi-analytical calculation method to find the low frequency value S I (0) of the spectral density of fluctuations of current through 1D arrays of small tunnel junctions, using the "orthodox theory" of single-electron tunneling. In all three array types studied, at low temperature (k B T ≪ eV ), increasing current induces a crossover from the Schottky value S I (0) = 2e Ī to the "reduced Schottky value" S I (0) = 2e Ī /N (where N is the array length) at some crossover current I c . In uniform arrays over a ground plane, I c is proportional to exp(−λN ), where λ −1 is the single-electron soliton length. In arrays without a ground plane, I c decreases slowly with both N and λ . Finally, we have calculated the statistics of I c for ensembles of arrays with random background charges.The standard deviation of I c from the ensemble average I c is quite large, typically between 0.5 and 0.7 of I c , while the dependence of I c on N or λ is so weak that it is hidden within the random fluctuations of the crossover current.73.40. Gk, 73.40.Rw, 85.40.Hp

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We have calculated the spatial distribution of the electrostatic potential created by an unbalanced charge q in one of the conducting electrodes of a long, uniform, linear array of small tunnel junctions. The distribution describes, in particular, the shape of a topological single-electron soliton in such an array. An analytical solution obtained for a circular cross section model is compared with results of geometrical modeling of a more realistic structure with square cross section. These solutions are very close to one another, and can be reasonably approximated by a simple phenomenological expression.