  Using the dynamical triangulation approach we perform a numerical study of a
supersymmetric random surface model that corresponds to the large N limit of
the four-dimensional version of the IKKT matrix model. We show that the
addition of fermionic degrees of freedom suppresses the spiky world-sheet
configurations that are responsible for the pathological behaviour of the
purely bosonic model. We observe that the distribution of the gyration radius
has a power-like tail p(R) ~ R^{-2.4}. We check numerically that when the
number of fermionic degrees of freedom is not susy-balanced, p(R) grows with
$R$ and the model is not well-defined. Numerical sampling of the configurations
in the tail of the distribution shows that the bosonic degrees of freedom
collapse to a one-dimensional tube with small transverse fluctuations. Assuming
that the vertex positions can fluctuate independently within the tube, we give
a theoretical argument which essentially explains the behaviour of p(R) in the
different cases, in particular predicting p(R) ~ R^{-3} in the supersymmetric
case. Extending the argument to six and ten dimensions, we predict p(R) ~
R^{-7} and p(R) ~ R^{-15}, respectively.
