The Aldous-Shields model revisited with application to cellular ageing
Title | The Aldous-Shields model revisited with application to cellular ageing |
Publication Type | Journal Article |
Year of Publication | 2010 |
Authors | Best, K, Pfaffelhuber, P |
Journal | Elec. Comm. Probab. |
Volume | 15 |
Start Page | 475 |
Pagination | 14 |
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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