  In models with large additional dimensions, the GUT scale can be lowered to
values accessible by future colliders. Due to modification of the loop
corrections from particles propagating into the extra dimensions, the
logarithmic running of the couplings of the Standard Model is turned into a
power law. These loop-correction are divergent and the standard way to achieve
finiteness is the introduction of a cut-off. The question remains, whether the
results are reliable as they depend on an unphysical parameter.
  In this paper, we show that this running of the coupling can be calculated
within a model including the existence of a minimal length scale. The minimal
length acts as a natural regulator and allows us to confirm cut-off
computations.
