# Mathematical Analysis for a Class of Stochastic Copolymerization Processes

## TL;DR

This paper provides a rigorous mathematical analysis of a stochastic copolymerization process, answering key questions about its behavior and extending results to more complex systems.

## Contribution

The paper introduces rigorous mathematical techniques to analyze and generalize stochastic copolymerization processes.

## Key findings

- Criteria for transience, null recurrence, and positive recurrence are established in terms of system parameters.
- Limiting fractions of monomer types in the transient regime are determined.
- The speed of polymer growth in the transient regime is quantified.

## Abstract

We study a stochastic model of a copolymerization process that has been extensively investigated in the physics literature. The main questions of interest include: (i) what are the criteria for transience, null recurrence, and positive recurrence in terms of the system parameters; (ii) in the transient regime, what are the limiting fractions of the different monomer types; and (iii) in the transient regime, what is the speed of growth of the polymer? Previous studies in the physics literature have addressed these questions using heuristic methods. Here, we utilize rigorous mathematical arguments to derive the results from the physics literature. Moreover, the techniques developed allow us to generalize to the copolymerization process with finitely many monomer types. We expect that the mathematical methods used and developed in this work will also enable the study of even more complex models in the future.