Large Deviation Principle for Occupancy Problems With Colored Balls
BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS
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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 1n 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.
- Statistics and Probability