Large Deviation Principle for Occupancy Problems With Colored Balls
Abstract
A Large Deviations Principle (LDP), demonstrated for occupancy problems with indistinguishable balls, is generalized to the case in which balls may be distinguished by a finite number of colors. The colors of the balls are chosen independently from the occupancy process itself. There are r balls thrown into n urns with the probability of a ball entering a given urn being 1/n (Maxwell-Boltzman statistics). The LDP applies with the scale parameter n going to infinity and the number of balls increasing proportionally. It holds under mild restrictions, the key one being that the coloring process by itself satisfies a LDP. Hence the results include the important special cases of deterministic coloring patterns and of colors chosen with fixed probabilities independently for each ball.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 06, 2003
- Accession Number
- ADA461905
Entities
People
- Carl Nuzman
- Paul Dupuis
- Phil Whiting
Organizations
- Brown University