ESSENTIAL ENHANCEMENTS IN ABELIAN NETWORKS: CONTINUITY AND UNIFORM STRICT MONOTONICITY

• 成果类型: Article
• 署名作者: Taggia, Lorenzo
• 署名单位: Sapienza University Rome
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1647
• 发表日期: 2023
• 页码: 2243-2264
• 关键词: activated random-walks; Stochastic dynamics; non-fixation; percolation; density; phase

摘要

We prove that in wide generality the critical curve of the activated random walk model is a continuous function of the deactivation rate, and we provide a bound on its slope, which is uniform with respect to the choice of the graph. Moreover, we derive strict monotonicity properties for the probability of a wide class of increasing events, extending previous results of (Invent. Math. 188 (2012) 127-150). Our proof method is of independent interest and can be viewed as a reformulation of the 'essential enhancements' technique, which was introduced for percolation, in the framework of abelian networks.