March 2011 A weakly 1-stable distribution for the number of random records and cuttings in split trees
Cecilia Holmgren
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Adv. in Appl. Probab. 43(1): 151-177 (March 2011). DOI: 10.1239/aap/1300198517


In this paper we study the number of random records in an arbitrary split tree (or, equivalently, the number of random cuttings required to eliminate the tree). We show that a classical limit theorem for the convergence of sums of triangular arrays to infinitely divisible distributions can be used to determine the distribution of this number. After normalization the distributions are shown to be asymptotically weakly 1-stable. This work is a generalization of our earlier results for the random binary search tree in Holmgren (2010), which is one specific case of split trees. Other important examples of split trees include m-ary search trees, quad trees, medians of (2k + 1)-trees, simplex trees, tries, and digital search trees.


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Cecilia Holmgren. "A weakly 1-stable distribution for the number of random records and cuttings in split trees." Adv. in Appl. Probab. 43 (1) 151 - 177, March 2011.


Published: March 2011
First available in Project Euclid: 15 March 2011

zbMATH: 1213.05037
MathSciNet: MR2761152
Digital Object Identifier: 10.1239/aap/1300198517

Primary: 05C05 , 05C80 , 68P10 , 68W40
Secondary: 60C05 , 60F05 , 68P05 , 68R10

Keywords: cut , infinitely divisible distribution , Random tree , record , split tree , stable distribution

Rights: Copyright © 2011 Applied Probability Trust


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Vol.43 • No. 1 • March 2011
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