Sharp thresholds for two-dimensional majority dynamics percolation
10th April 2020, 3:30 pm – 4:30 pm
In two-dimensional majority dynamics, each vertex starts with an i.i.d. Bernoulli(p) initial opinion that can be either zero or one. Independently with rate one, each vertex updates its opinion to coincide with the majority of its neighbors. Ties are broken by maintaining the original opinion of the vertex. We study the percolation process arising from the configuration obtained by running majority dynamics up to time t. We prove that box crossing events undergo a sharp phase transition when varying the initial density p. Based on a joint work with C. Alves.