  Seven and a half years of continuous monitoring of giant air showers
triggered by ultra high-energy cosmic rays have been recently summarized by the
AGASA collaboration. The resulting energy spectrum indicates clearly that the
cosmic ray spectrum extends well beyond the Greisen-Zatsepin-Kuzmin (GZK)
cut-off at $\sim 5 \times 10^{19}$ eV. Furthermore, despite the small number
statistics involved, some structure in the spectrum may be emerging. Using
numerical simulations, it is demonstrated in the present work that these
features are consistent with a spatial distribution of sources that follows the
distribution of luminous matter in the local Universe. Therefore, from this
point of view, there is no need for a second high-energy component of cosmic
rays dominating the spectrum beyond the GZK cut-off.
