On a linear polymerisation process

Paper in proceeding, 2020

We consider a Markov fusion-disaggregation process of 'molecules' which are linear arrangements of 'atoms'. Molecules may fuse at the ending atoms by creating a bond in between at a given rate. Each bond joining two atoms in a molecule can break so that a molecule disaggregates into two shorter molecules at another rate. We give en explicit expression for the stationary distribution of the number of molecules and the conditional distribution of their lengths given their number. We show an asymptotic normality of the distribution of the number of molecules when the number of atoms in the system grows.