Open Access
May 2002 Bins and balls; Large deviations of the empirical occupancy process
Stéphane Boucheron, Fabrice Gamboa, Christian Léonard
Ann. Appl. Probab. 12(2): 607-636 (May 2002). DOI: 10.1214/aoap/1026915618


In the random allocation model, balls are sequentially inserted at random into $n$ exchangeable bins. The occupancy score of a bin denotes the number of balls inserted in this bin. The (random) distribution of occupancy scores defines the object of this paper: the empirical occupancy measure which is a probability measure over the integers. This measure-valued random variable packages many useful statistics. This paper characterizes the large deviations of the flow of empirical occupancy measures when $n$ goes to infinity while the number of inserted balls remains proportional to $n$. The main result is a Sanov-like theorem for the empirical occupancy measure when the set of probability measures over the integers is endowed with metrics that are slightly stronger than the total variation distance. Thanks to a coupling argument, this result applies to the degree distribution of sparse random graphs.


Download Citation

Stéphane Boucheron. Fabrice Gamboa. Christian Léonard. "Bins and balls; Large deviations of the empirical occupancy process." Ann. Appl. Probab. 12 (2) 607 - 636, May 2002.


Published: May 2002
First available in Project Euclid: 17 July 2002

zbMATH: 1013.60017
MathSciNet: MR1910642
Digital Object Identifier: 10.1214/aoap/1026915618

Primary: 05A17 , 05C40 , 60F10
Secondary: 05A99 , 05C80

Keywords: large deviations , occupancy , Orlicz spaces , Poisson approximation , Random graphs , Sanov theorem

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.12 • No. 2 • May 2002
Back to Top