Local density of point-source activated random walk on ℤ

Activated random walk (ARW) is an interacting particle system that is a leading candidate for a rigorous theory of self-organized criticality. We study one-dimensional ARW on ℤ started from a point source n\delta_0, and prove that uniformly throughout a macroscopic window around the source, the probability that a given site contains a sleeping particle after stabilization is asymptotically the critical density \rho_c. Our approach combines a coupling of neighboring one-dimensional IDLA clusters with a reduction of bulk blocks to a driven-dissipative ARW via boundary flux counts. Joint work with Christopher Hoffman and Jacob Richey.