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Strong Convergence of Partial Match Queries in Random Quadtrees

Published online by Cambridge University Press:  27 April 2012

NICOLAS CURIEN
NICOLAS CURIEN*
Affiliation:
Département de Mathématiques et Applications, École Normale Supérieure, 45 rue d'Ulm, 75230 Paris CEDEX 05, France (e-mail: nicolas.curien@ens.fr)
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Abstract

We prove that the rescaled costs of partial match queries in a random two-dimensional quadtree converge almost surely towards a random limit which is identified as the terminal value of a martingale. Our approach shares many similarities with the theory of self-similar fragmentations.

Keywords

Primary 60F9960G4460G1868W40
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 5 , September 2012 , pp. 683 - 694
Copyright
Copyright © Cambridge University Press 2012

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