  We investigate inflation in a multi-dimensional landscape with a hierarchy of
energy scales, motivated by the string theory, where the energy scale of Kahler
moduli is usually assumed to be much lower than that of complex structure
moduli and dilaton field. We argue that in such a landscape, the dynamics of
slow-roll inflation is governed by the low-energy potential, while the initial
condition for inflation are determined by tunneling through high-energy
barriers. We then use the scale factor cutoff measure to calculate the
probability distribution for the number of inflationary e-folds and the
amplitude of density fluctuations $Q$, assuming that the low-energy landscape
is described by a random Gaussian potential with a correlation length much
smaller than $M_{\rm pl}$. We find that the distribution for $Q$ has a unique
shape and a preferred domain, which depends on the parameters of the low-energy
landscape. We discuss some observational implications of this distribution and
the constraints it imposes on the landscape parameters.
