  We implement fermions on dynamical random triangulation and determine
numerically the spectrum of the Dirac-Wilson operator D for the system of
Majorana fermions coupled to two-dimensional Euclidean quantum gravity. We
study the dependence of the spectrum of the operator (epsilon D) on the hopping
parameter. We find that the distributions of the lowest eigenvalues become
discrete when the hopping parameter approaches the value 1/sqrt{3}. We show
that this phenomenon is related to the behavior of the system in the
'antiferromagnetic' phase of the corresponding Ising model. Using finite size
analysis we determine critical exponents controlling the scaling of the lowest
eigenvalue of the spectrum including the Hausdorff dimension d_H and the
exponent kappa which tells us how fast the pseudo-critical value of the hopping
parameter approaches its infinite volume limit.
