Research  

Anderson, D. F., Ma, J., Gagrani, P. Mathematical Analysis for a Class of Stochastic Copolymerization Processes. Preprint, arXiv:2510.05383 [math.PR], 2025.

Abstract: In this work, we study a simple copolymerization model in which a set of monomers attach to or detach from the tip of a polymer. We also assume that the binding and unbinding rates (affinities) for the different monomers are different, but fixed (i.e., do not depend upon the rest of the polymer chain). By recasting the dynamics as a continuous-time Markov process on an infinite tree-like state space, we establish recurrence and transience criteria, and derive almost-sure laws for polymer growth and composition using the theory of Markov chains on trees with finitely many "cone types".

Low Variance Couplings for Multivariate Parameter Sensitivity in Stochastic Chemical Reaction Networks.  In Progress.