2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159363We investigate a model of cell division in which the length of telomeres within the cell regulate their proliferative potential. At each cell division the ends of linear chromosomes change and a cell becomes senescent when one or more of its telomeres become shorter than a critical length. In addition to this systematic shortening, exchange of telomere DNA between the two daughter cells can occur at each cell division. We map this telomere dynamics onto a biased branching diffusion process with an absorbing boundary condition whenever any telomere reaches the critical length. As the relative effects of telomere shortening and cell division are varied, there is a phase transition between finite lifetime and infinite proliferation of the cell population. Using simple first-passage ideas, we quantify the nature of this transition.6 pages, 1 figure, 2-column revtex4 format; version 2: final published form; contains various improvements in response to referee commentsCell BehaviorStatistical MechanicsBiological Physicstext