The limiting density of the positive spins for majority dynamics on 3-regular tree has no jumps
We consider the majority dynamics on the infinite 3-regular tree, where each vertex has an i.i.d. Poisson clock attached to it, and when the clock of a vertex rings, the vertex looks at the spins of its three neighbors and flips its spin, if necessary, to come into agreement with majority of its neighbors. The initial spins of the vertices are taken to be i.i.d. Bernoulli random variables with parameter p. We show that the probability that the limiting spin at the root is + is continuous with respect to the initial bias p. Our argument relies upon mass transport principle. The talk is based on an ongoing work with M. Damron.