Kinetic Description of Social Dynamics: From Consensus to Flocking

Some simple kinetic models of information-exchange processes

Irene Gamba

University of Texas at Austin

In this talk we will discuss some models of information-exchange processes on a large network. The general context of its global behavior is dictated by three factors: the geometry of the network, the nature of interactions between agents whose informational state is referred as 'type' (interaction laws dictate how the type of an agent changes upon meeting with other agents), and the initial distribution of information. Each plays a significant role in determining asymptotic states, which can be interpreted with probabilistic methods, based on techniques pertaining to the classical central limit problem and fixed–point equations for probability distributions. In particular, we study the domain of attraction to stable distributions (self–similar or fixed points in the solution space) depending the initial data. Moreover, the speed of convergence are given in terms of Kantorovich-Wasserstein and Zolotarev distances between probability measures.
This is work in collaboration with Ravi Srinivasan