  The scaling property of level statistics in the quantum Hall regime, i.e. 2D
disordered electron systems subject to strong magnetic fields, is analyzed
numerically in the light of the random matrix theory. The energy dependences of
the effective level repulsion parameter, the two level correlation, the GUE-GOE
crossover parameter, and the rigidity (or $\Delta_3$-statistics) of the level
distributions are investigated for different system sizes by unfolding the
original data and by dividing the unfolded spectrum into small regions. It is
shown that the critical exponent of the localization length as a function of
energy can be determined through the energy dependence of the level statistics.
The analyses are carried out not only for the lowest Landau band (LB) but also
for the second lowest LB. Furthermore the effect of finite range of disordered
potential is studied. The short-ranged potential case in the second lowest LB
is found to be pathological as in other studies of critical behavior, and it is
confirmed that this pathological behavior is improved in the case of disordered
potential with finite ranges.
