Jinsu Kim, University of Wisconsin-Madison
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MGH 085
Title : Stochastically modeled reaction networks: Stationary distribution and mixing times.
Abstract : Reaction networks are graphical configurations that can be used to describe biological interaction networks. If the abundances of the constituent species of the system are low, we can model the dynamics of species counts in a jump by jump fashion as a continuous-time Markov chain. In this talk, we will mainly focus on which underlying structures of the networks imply existence of a stationary distribution for the continuous-time Markov chain associated to the stochastically modeled reaction networks. I will also present results related to their mixing times, which give the time required for the distribution of the continuous-time Markov chain to get close to the stationary distribution.