Open Access
2010 The Aldous-Shields model revisited with application to cellular ageing
Katharina Best, Peter Pfaffelhuber
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Electron. Commun. Probab. 15: 475-488 (2010). DOI: 10.1214/ECP.v15-1581


In Aldous and Shields (1988) a model for a rooted, growing random binary tree with edge lengths 1 was presented. For some $c>0$, an external vertex splits at rate $c^{-i}$ (and becomes internal) if its distance from the root (depth) is $i$. We reanalyse the tree profile for $c>1$, i.e. the numbers of external vertices in depth $i=1,2,...$. Our main result are concrete formulas for the expectation and covariance-structure of the profile. In addition, we present the application of the model to cellular ageing. Here, we say that nodes in depth $h+1$ are senescent, i.e. do not split. We obtain a limit result for the proportion of non-senesced vertices for large $h$.


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Katharina Best. Peter Pfaffelhuber. "The Aldous-Shields model revisited with application to cellular ageing." Electron. Commun. Probab. 15 475 - 488, 2010.


Accepted: 19 October 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1226.60129
MathSciNet: MR2733372
Digital Object Identifier: 10.1214/ECP.v15-1581

Primary: 60K35
Secondary: 05C0 , 60J85 , 92D20

Keywords: cellular senescence , Hayflick limit , Random tree , telomere

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