Mathematical Analysis for a Class of Stochastic Copolymerization Processes
by Lukas Eigentler and Mattia Sensi.
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Self-replicating polymers that encode genetic information are central to the origin of biological information. We study a stochastic model of a copolymerization process in which finitely many monomer types attach to or detach from the tip of a polymer, with distinct but fixed binding affinities. We determine a sharp criterion for when the process is recurrent (the polymer length fluctuates around a finite value) or transient (the polymer length diverges to infinity). In the transient case, we characterize both the long-term composition of the polymer and its rate of growth. We place these results on a rigorous probabilistic foundation that provides a precise derivation of predictions from earlier work and enables further generalizations.
