Research  

Papers

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

Abstract: Life’s origins hinge on how long information-carrying polymers (RNA/DNA) grow by adding monomers—i.e., copolymerization. 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 attaching and detaching rates 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.

Colloquium, Seminars, and Conference Talks

• Stochastic Reaction Networks Workshop — June 16, 2025 — Politecnico di Torino

       Topic: Mathematical Analysis for a Class of Stochastic Copolymerization Processes

• SIAM Conference on Applied Algebraic Geometry (AG25) — July 11, 2025 — University of Wisconsin–Madison

       Topic: Mathematical Analysis for a Class of Stochastic Copolymerization Processes

• Seminar on the Mathematics of Reaction Networks — October 23, 2025 — Online

       Topic: Mathematical Analysis for a Class of Stochastic Copolymerization Processes