Essential enhancements in Abelian networks: continuity and uniform strict monotonicity

26 Apr 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)... (read more)

PDF Abstract
No code implementations yet. Submit your code now

Categories


  • PROBABILITY
  • MATHEMATICAL PHYSICS
  • MATHEMATICAL PHYSICS