  In this paper, we investigate the effect of supersymmetry on the symmetry
classification of random matrix theory ensembles. We mainly consider the random
matrix behaviors in the $\mathcal{N}=1$ supersymmetric generalization of the
Sachdev-Ye-Kitaev (SYK) model, a toy model for the two-dimensional quantum
black hole with supersymmetric constraint. Some analytical arguments and
numerical results are given to show that the statistics of the supersymmetric
SYK model could be interpreted as random matrix theory ensembles, with a
different eight-fold classification from the original SYK model and some new
features. The time-dependent evolution of the spectral form factor is also
investigated, where predictions from random matrix theory are governing the
late time behavior of the chaotic Hamiltonian with supersymmetry.
