Recent results on the phase transition for activated random walk.
In this talk I will discuss activated random walk, an interacting particle system that exhibits a phase transition on infinite domains and self-organized criticality on finite domains. In the infinite version, the system is initialized with density $\mu$ of particles which perform independent simple random walk, fall asleep at rate $\lambda$, and are woken up if another particle moves to the same site. There are two possible limiting behaviors: local fixation, where each site is visited finitely many times a.s., or non-fixation, where each site is visited infinitely many times a.s. Current research is focused on determining where the transition between these two phenomena occurs in terms of $\mu$ and $\lambda$. I will present some recent results and discuss the novel tools involved.