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On the Variety of Shapes on the Fringe of a Random Recursive Tree

Published online by Cambridge University Press:  14 July 2016

Qunqiang Feng*
Affiliation:
University of Science and Technology of China
Hosam M. Mahmoud*
Affiliation:
The George Washington University
*
Postal address: Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China. Email address: [email protected]
∗∗Postal address: Department of Statistics, The George Washington University, Washington, DC 20052, USA. Email address: [email protected]
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Abstract

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We consider a variety of subtrees of various shapes lying on the fringe of a recursive tree. We prove that (under suitable normalization) the number of isomorphic images of a given fixed tree shape on the fringe of the recursive tree is asymptotically Gaussian. The parameters of the asymptotic normal distribution involve the shape functional of the given tree. The proof uses the contraction method.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2010 

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