# Stochatically modeled reaction networks : positive recurrence and mixing times.

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A reaction network is a graphical configuration that describes an interaction between species (molecules). If the abundances of the network system is small, then the randomness inherent in the molecular

interactions is important to the system dynamics, and the abundances are modeled stochastically as a jump by jump fashion continuous-time Markov chain. One of challenging issues facing researchers who study biological

systems is the often extraordinarily complicated structure of their interaction networks. Thus, how to characterize network structures that induce characteristic behaviors of the system dynamics is one of the major open questions in this literature.

In this talk, I will provide an analytic approach to find a class of reaction networks whose associated Markov process has a stationary distribution. Moreover I will talk about the convergence rate for the process to its stationary distribution with the mixing time.