@article {14,
title = {The Aldous-Shields model revisited with application to cellular ageing},
journal = {Elec. Comm. Probab.},
volume = {15},
year = {2010},
pages = {14},
chapter = {475},
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.},
author = {Katharina Best and Pfaffelhuber, Peter}
}