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    Essential enhancements in Abelian networks: Continuity and uniform strict monotonicity
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Taggi, Lorenzo
    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.