Abstract:

In this paper, the near-critical and super-critical asymptoticbehavior of a reversible
Markov process as a chemical model for polymerizationwas studied. The results of
the present paper, together with an analysis ofthe sub-criticalstage, establish the existence
of three distinct stages (sub-critical, near-criticaland super-critical stages) of polymerization
(in the thermodynamic limit as N → +∞ ),depending on the value of strength of
the fragmentation reaction. These three stages correspond to the size of the largest length
of polymers of size N to be itself of order logN, N
m
m+1 (m ≥ 2,m 6= 4n, n ≥ 1) and N,
respectively.

Key words: Polymerization, Markov process, limit behavior, stationary distribution