We investigate the current-current correlations in a four-terminal Al-AlOx-Al tunnel junction where shot noise dominates. We demonstrate that cross-correlations in the presence of two biasing sources of the Hanbury-Brown and Twiss type are much stronger (approximately twice) than an incoherent sum of correlations generated by single sources. The difference is due to voltage fluctuations of the central island that give rise to current-current correlations in the four contacts of the junction. Our measurements are in close agreement with results obtained using a simple theoretical model based on the theory of shot noise in multi-terminal conductors, generalized here to arbitrary contacts.
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