Georgia Institute of Technology College of Sciences

In the continuous-time majority vote model, each vertex of a graph is initially assigned an ``opinion,'' either 0 or 1. At exponential times, vertices update their values by assuming the majority value of their neighbors. This model has been studied extensively on Z^d, where it is known as the zero-temperature limit of Ising Glauber dynamics. I will review some of the major questions and conjectures on lattices, and then explain some new work with Arnab Sen (Minnesota) on the 3-regular tree. We relate the majority vote model to a new model, which we call the median process, and use this process to answer questions about the limiting state of opinions. For example, we show that when the initial state is given by a Bernoulli(p) product measure, the probability that a vertex's limiting opinion is 1 is a continuous function of p.