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arXiv · 1004.1581

The Aldous-Shields model revisited (with application to cellular ageing)

Katharina Best·Peter Pfaffelhuber
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Abstract

In Aldous and Shields (1988), a model for a rooted, growing random binary tree 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. For c>1, we reanalyse the tree profile, 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 assume that nodes in depth h+1 are senescent, i.e. do not split. We obtain a limit result for the proportion of non-senescent vertices for large h.

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Katharina Best, Peter Pfaffelhuber. 2010-04-09. The Aldous-Shields model revisited (with application to cellular ageing). https://arxiv.org/abs/1004.1581

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