Absorbing-state phase transition in biased activated random walk

作者：Taggi Lorenzo^*

来源：Electronic Journal of Probability, 2016, 21(0): 13.

DOI：10.1214/16-EJP4275

• interacting particles
• activated random walk
• lattice gasses
• Abelian networks

We consider the activated random walk model on Z(d), 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 mu(c). We prove that if the jump distribution is biased, then mu(c) < 1 for any sleeping rate lambda, d >= 1, and that mu(c) -> 0 as lambda -> 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.

• 出版日期2016