Collective dynamics and model verification: Connecting kinetic modeling to data

Limits of stochastic binary interactions on a dense graph

Juan Rodriguez

University of Texas at Austin


Homogeneous Boltzmann-like equations have recently been used to model the evolution of wealth, opinions or information among a population of agents interacting in groups over time. These equations do not take into account a possible underlying network structure constraining agent interactions. We derive a kinetic collisional equation for stochastic binary interaction Markov jump processes occurring on a dense graph. This is achieved through the use of graphons, the limit objects for dense graphs. We present examples of the equation for wealth exchange and opinion dynamics models.