  We develope a computationally efficient extension of the Dyson Brownian
Motion (DBM) algorithm to generate random function in C2 locally. We further
explain that random functions generated via DBM show an unstable growth as the
traversed distance increases. This feature restricts the use of such functions
considerably if they are to be used to model globally defined ones. The latter
is the case if one uses random functions to model landscapes in string theory.
We provide a concrete example, based on a simple axionic potential often used
in cosmology, to highlight this problem and also offer an ad hoc modification
of DBM that suppresses this growth to some degree.
