  There has been recently a lot of research on sparse variants of random
projections, faster adaptations of the state-of-the-art dimensionality
reduction technique originally due to Johsnon and Lindenstrauss. Although the
construction is very simple, its analyses are notoriously complicated. Meeting
the demand for both simplicity and accuracy, this work establishes sharp
sub-poissonian tail bounds for the distribution of sparse random projections.
Compared to other works, this analysis provide superior numerical guarantees
(exactly matching impossibility results) while being arguably less complicated
(the technique resembles Bennet's Inequality and is of independent interest).
