  We compute the distribution of minima that are reached dynamically on
multi-field axionic landscapes, both numerically and analytically. Such
landscapes are well suited for inflationary model building due to the presence
of shift symmetries and possible alignment effects (the KNP mechanism). The
resulting distribution of dynamically reached minima differs considerably from
the naive expectation based on counting all vacua. These differences are more
pronounced in the presence of many fields due to dynamical selection effects:
while low lying minima are preferred as fields roll down the potential,
trajectories are also more likely to get trapped by one of the many nearby
minima. We show that common analytic arguments based on random matrix theory in
the large $D$-limit to estimate the distribution of minima are insufficient for
quantitative arguments pertaining to the dynamically reached ones. This
discrepancy is not restricted to axionic potentials. We provide an empirical
expression for the expectation value of such dynamically reached minimas'
height and argue that the cosmological constant problem is not alleviated in
the absence of anthropic arguments. We further comment on the likelihood of
inflation on axionic landscapes in the large D-limit.
