4 problems

Consider majority dynamics on $\mathbb{Z}^2$ with i.i.d. initial opinions of density $p\in[0,1]$, and let $\eta_t(0)$ denote the opinion at the origin at time $t$. Exponential fixa…

Consider the zero-temperature stochastic Ising model on $\mathds{Z}^d$, $d\thickspace\in\mathds{N}^*$, with each site initially independently in state $+$ with probability…

Let $(\eta_t)_{t\geq0}$ be median dynamics and, for an initial density $p\in[0,1]$, let $(\xi_t^p)_{t\geq0}$ be the coupled majority-dynamics process. Say that majority dynamics fi…

Let $(\xi_t)_{t\geq 0}$ be zero-temperature Glauber dynamics on $\mathbb{Z}^d$, and define … Here $\tilde{p}_c(d)$ is the threshold for fixation at opinion $1$. Fixation-threshold…