STOR Colloquium: Yu-Ting Chen, Harvard University

Stochastic interacting systems on graphs

For more realistic modeling, there have been significant interests for the use of general graphs for interacting particle systems arising from biological or social contexts. However, the generality of spatial structure can lead to fundamental issues. They include the missing link to the stochastic PDE method that can give very detailed and clean information of interacting particle systems after rescaling, and the question of which graph parameters are essential to describe certain probability laws of interest.
In this talk, I will discuss voter models and related methods, with an emphasis on the context of general graphs. I will demonstrate recent progress for some questions from Aldous for voter models and the so-called benefit-to-cost ratios first discovered by Ohtsuki, Hauert, Lieberman, and Nowak for evolutionary games that are variants of voter models. In particular, I will explain some diffusion approximation results for voter models on general graphs, which may provide new insights for related interacting particle systems on large graphs.