Absorbing-state phase transition in biased activated random walk
Absorbing-state phase transition in biased activated random walk
复制标题
偏置激活随机游走中的吸收态相变
DOI：
10.1214/16-ejp4275
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
L. Taggi
中科院分区：
文献类型：
--
作者：
L. Taggi
我们考虑了$\mathbb{Z}^d$上的激活随机游走模型，该模型经历了从吸收区到持续活动区的过渡。在任何维度上，我们证明了当粒子密度小于1时，只要跳跃分布是有偏的，并且睡眠率足够小，系统就处于活动状态。这回答了Rolla and Sidoravicius（2012）和Dickman，Rolla and Sidoravicius（2010）在有偏跳跃分布情况下的一个问题。此外，我们证明了临界密度依赖于跳跃分布。
We consider the activated random walk (ARW) model on $\mathbb{Z}^d$, which undergoes a transition from an absorbing regime to a regime of sustained activity. In any dimension we prove that the system is in the active regime when the particle density is less than one, provided that the jump distribution is biased and that the sleeping rate is small enough. 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.