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Large Deviations Principle for Occupancy Problems with Colored Balls

  • Paul Dupuis (a1), Carl Nuzman (a2) and Phil Whiting (a2)

Abstract

A large deviations principle (LDP), demonstrated for occupancy problems with indistinguishable balls, is generalized to the case in which balls are 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 (i.e. Maxwell-Boltzmann statistics). The LDP applies with the scale parameter, n, tending to infinity and r increasing proportionally. The LDP holds under mild restrictions, the key one being that the coloring process by itself satisfies an LDP. This includes the important special cases of deterministic coloring patterns and colors chosen with fixed probabilities independently for each ball.

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Copyright

Corresponding author

Research supported in part by the National Science Foundation (NSF-DMS-0306070 and NSF-DMS-0404806) and the Army Research Office (DAAD19-02-1-0425).
∗∗ Postal address: Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA.
∗∗∗ Postal address: Bell Labs, Alcatel-Lucent, 600 Mountain Avenue, Murray Hill, NJ 07974, USA.
∗∗∗∗ Email address: pwhiting@research.bell-labs.com

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Large Deviations Principle for Occupancy Problems with Colored Balls

  • Paul Dupuis (a1), Carl Nuzman (a2) and Phil Whiting (a2)

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