|Min Kang (강민정)
|North Carolina State University
Consider a conservative interacting particle system on a domain whose branching mechanism is triggered by contact with a set. The law governing the motion of individual particle together with a boundary condition given by the catalyst gives rise to a quasi-stationary distribution (QSD). We clarify how the catalytic random particle system above relates to the QSD. Then we discuss why acquiring the QSD is so essential in understanding underlying Markov structure behind the motion (infinitesimal generator), which leads to a variety of applications including the study of large social networks. The catalytic particle system provides a reliable novel way to approximate the QSD which casts insight into large graph structures and their spectrum.