Electronic Communications in Probability

The Aldous-Shields model revisited with application to cellular ageing

Katharina Best and Peter Pfaffelhuber

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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 $h$.

Article information

Electron. Commun. Probab. Volume 15 (2010), paper no. 43, 475-488.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 92D20: Protein sequences, DNA sequences 60J85: Applications of branching processes [See also 92Dxx] 05C0

Random tree cellular senescence telomere Hayflick limit

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Best, Katharina; Pfaffelhuber, Peter. The Aldous-Shields model revisited with application to cellular ageing. Electron. Commun. Probab. 15 (2010), paper no. 43, 475--488. doi:10.1214/ECP.v15-1581. https://projecteuclid.org/euclid.ecp/1465243986

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