Refined Large Deviation Asymptotics for the Classical Occupancy Problem

In this paper refined large deviation asymptotics are derived for the classical occupancy problem. The asymptotics are established for a sequential filling experiment and an occupancy experiment. In the first case the random variable of interest is the number of balls required to fill a given fraction of the urns, while in the second a fixed number of balls are thrown and random variable is the fraction of nonempty urns.