Absorbing-state phase transition in biased activated random walk

We consider the activated random walk model on ℤd, which undergoes a transition from an absorbing regime to a regime of sustained activity. A central question for this model involves the estimation of the critical density μc. We prove that if the jump distribution is biased, then μc < 1 for any sleeping rate λ, d ≥ 1, and that μc → 0 as λ → 0 in one dimension. This answers a question from Rolla and Sidoravicius (2012) and Dickman, Rolla and Sidoravicius (2010) in the case of biased jump distribution. Furthermore, we prove that the critical density depends on the jump distribution.