  This paper studies the effect of truncation on the large deviations behavior
of the partial sum of a triangular array coming from a truncated power law
model. Each row of the triangular array consists of i.i.d. random vectors,
whose distribution matches a power law on a ball of radius going to infinity,
and outside that it has a light-tailed modification. The random vectors are
assumed to be R^d-valued. It turns out that there are two regimes depending on
the growth rate of the truncating threshold, so that in one regime, much of the
heavy tailedness is retained, while in the other regime, the same is lost.
