@article{ECP1581,
author = {Katharina Best and Peter Pfaffelhuber},
title = {The Aldous-Shields model revisited with application to cellular ageing},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {15},
year = {2010},
keywords = {Random tree; cellular senescence; telomere; Hayflick limit},
abstract = {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 $h$.},
pages = {no. 43, 475-488},
issn = {1083-589X},
doi = {10.1214/ECP.v15-1581},
url = {http://ecp.ejpecp.org/article/view/1581}}