Mean field limits by population acceleration

Harsha Honnappa, Rahul Jain, Amy R. Ward

Abstract: Mean field or large population limits are useful analytical tools that provide well justified approximations to finite systems. Motivated by problems in Game Theory and Queueing Theory we provide a framework to develop mean field limits that emerge from finite population systems in a very general setting. Our results prove new generalizations of the standard Glivenko-Cantelli and Donsker's Theorems. We prove these limits by making use of an analytical technique called population acceleration first introduced in [1] to study transtitory queueing models.