Essential enhancements in Abelian networks: continuity and uniform strict monotonicity

Lorenzo Taggi

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arXiv · 2003.00932

Essential enhancements in Abelian networks: continuity and uniform strict monotonicity

Lorenzo Taggi

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Abstract

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 Rolla and Sidoravicius (2012). 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.

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Lorenzo Taggi. 2020-03-02. Essential enhancements in Abelian networks: continuity and uniform strict monotonicity. https://arxiv.org/abs/2003.00932

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