  Motivated by the string landscape, inflation may happen on a high dimensional
complicated potential. We propose a new way to construct some high dimensional
random potentials, and study inflation on top of that, for up to 50-dimensions
in field space. Especially, random bifurcations of classical inflationary
trajectory are studied. It is shown that the bifurcation probability increases
as a function of number of dimensions. Those random bifurcations are not
consistent with observations, and dramatically limit the parameter space of
inflation on a complicated landscape. For example, in 10 dimensions, only
$10^{-3} \sim 10^{-6}$ of the parameter space volume leads to unique classical
trajectories. The rest is ruled out by random bifurcations.
