  The type IIB matrix model is one of the most promising candidates for a
nonperturbative formulation of superstring theory. In particular, its
Lorentzian version was shown to exhibit an interesting real-time dynamics such
as the spontaneous breaking of the 9-dimensional rotational symmetry to the
3-dimensional one. This result, however, was obtained after regularizing the
original matrix integration by introducing "infrared" cutoffs on the quadratic
moments of the Hermitian matrices. In this paper, we generalize the form of the
cutoffs in such a way that it involves an arbitrary power ($2p$) of the
matrices. By performing Monte Carlo simulation of a simplified model, we find
that the results become independent of $p$ and hence universal for $p \gtrsim
1.3$. For $p$ as large as 2.0, however, we find that large-$N$ scaling
behaviors do not show up, and we cannot take a sensible large-$N$ limit. Thus
we find that there is a certain range of $p$ in which a universal large-$N$
limit can be taken. Within this range of $p$, the dynamical space-time
dimensionality turns out to be $(3+1)$, while for $p=2.0$, where we cannot take
a sensible large-$N$ limit, we observe a (5+1)d structure.
