Accession Number:

ADA461986

Title:

Large Deviation Principle for General Occupancy Models (Preprint)

Descriptive Note:

Journal article

Corporate Author:

BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS

Personal Author(s):

Report Date:

2004-12-01

Pagination or Media Count:

25.0

Abstract:

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 urns contents prior to the throw. We discuss a parametric family of statistical models which includes Maxwell-Boltzmann, Bose-Einstein 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.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE