Probability Seminar
Fix a $p\in(0,1)$ and consider the following Markov chain on $\{0,1\}^{\mathbb{Z}}$: each vertex $v$, independently of the others, tries to refresh its value with a $\textrm{Bernoulli}(p)$ variable at rate $1$. The new value is accepted iff the left neighbor is $0$. This is the East Model, first studied rigorously by Aldous and Diaconis. The above is just an example of a constrained spin model. These form a general class of chains used to mimic "glassy" dynamics in the physics literature where the local update of a spin occurs only in the presence of a special ("facilitating") configuration at neighboring vertices. In this talk we will establish cutoff with an optimal window size for the East model on finite intervals with frozen boundary conditions. We will end with some interesting open problems. The talk is based on joint work with Eyal Lubetzky and Fabio Martinelli.