Large Deviation Principle for General Occupancy Models

We use process level large deviation analysis to obtain the rate function for a general family of occupancy problems. Our interest is the asymptotics of the empirical distributions of various quantities (such as the fraction of urns that contain a given number of balls). In the general setting, balls are allowed to land in a given urn depending on the urn’s contents prior to the throw. We discuss a parametric family of statistical models which includes Maxwell-Boltzmann, BoseEinstein and Fermi-Dirac statistics as special cases. A process level large deviation analysis is conducted and the rate function for the original problem is then characterized, via the contraction principle, by the solution to a calculus of variations problem. We conjecture that the solution to the variational problem coincides with that of a finite dimensional minimization problem.