Generalized Hammersley Process and Phase Transition for Activated Random Walk Models

Understand

* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution.

• Active particles perform random walks without interaction, and they may as well change their state to passive, then stopping to jump.
• When particles of both types occupy the same site, they all become active.
• This model exhibits phase transition in the sense that for low initial densities the system locally fixates and for high densities it keeps active.