Title: Dynamical noise sensitivity of the Voter and Campaign models

Abstract: In the voter model, each vertex  v on a graph is given some initial opinion a_v(0), and opinions evolve with time by interactions between neighboring vertices in which one side convinces the other.  It is not hard to see that on a finite graph, the system will eventually reach a consensus, which can be seen as the output of this system. The classical notion of noise sensitivity of a Boolean function asks how much is the output of the function sensitive to small (random) perturbations in its input. 

In this talk we introduce the notion of dynamical noise sensitivity, which studies how much is the output of an opinion dynamics model (such as the voter model) sensitive to small perturbations in the dynamics, that is to changing a small portion of the interactions. 

After analyzing the voter model, we will discuss a current work in progress on a generalization of the voter model that we call the campaign model, in which people interact as in the voter model but for a limited amount of time ("the campaign")  and then a majority vote it taken ("elections"). This model depends much more crucially on the geometry of the underlying graph and exhibits a non-trivial phase transition in terms of the dynamical noise sensitivity. 

The talk is based on joint works with Omer Angel, Rangel Baldasso, Guy Blachar,  Daniel de-la Riva  , Omri Marcus and  Ron Peretz.

Livestream/Recording: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=3b190361-7c1c-4f0d-8742-b1a2005bce28