General urn models with several types of balls and Gaussian limiting fields

Authors:
Michael Drmota;Danièle Gardy;Bernhard Gittenberger
Affiliations:
Department of Geometry, Technische Universität Wien, Wiedner Hauptstraße 8-10/113, A-1040 Wien, Austria;PRISM, CNRS UMR 8636 and Université de Versailles Saint-Quentin, 78035 Versailles Cedex, France;Department of Geometry, Technische Universität Wien, Wiedner Hauptstraße 8-10/113, A-1040 Wien, Austria
Venue:
Random Structures & Algorithms
Year:
2004

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Abstract

We study a system of m urns, where several types of balls are thrown, and an additive valuation is assigned to each urn depending on its state. Examples are the join models studied in a database context, and some models with two types of balls. The object of our investigation is the evolution of the valuation with time, when a ball is thrown at each time unit. By means of a generating function approach we show the weak convergence of the valuation process to a Gaussian field.