The density conjecture for activated random walk
arxiv(2024)
Abstract
In the late 1990s, Dickman, Muñoz, Vespignani, and Zapperi explained the
self-organized criticality observed by Bak, Tang, and Wiesenfeld as an external
force pushing a hidden parameter toward the critical value of a traditional
absorbing-state phase transition. As evidence, they observed empirically that
for various sandpile models the particle density in a finite box under
driven-dissipative dynamics converges to the critical density of an
infinite-volume version of the model. We give the first proof of this
well-known density conjecture in any setting by establishing it for activated
random walk in one dimension. We prove that two other natural versions of the
model have the same critical value, further establishing activated random walk
as a universal model of self-organized criticality.
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