World Congress in Probability and Statistics

Stationary distributions and graphical equilibria in Reaction Networks Theory

Chemical reaction networks can be modelled either deterministically, by means of a system of ordinary differential equations, or stochastically, by means of a continuous time Markov chain. The relationship between steady states of the deterministic model with graphical properties of the network have been intensively studied since the Seventies, with a special focus on complex balanced equilibria. However, a similar analysis for stationary distributions in the stochastic setting was not available. We introduce the notion of complex balanced stationary distribution and study the link between this notion and that of complex balanced equilibrium. We further explore more detailed relationships between graphical equilibria in the deterministic and stochastic settings.