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On the slow phase for fixed-energy Activated Random Walks (2408.07049v1)
Published 13 Aug 2024 in math.PR
Abstract: We study the Activated Random Walk model on the one-dimensional ring, in the high density regime. We develop a toppling procedure that gradually builds an environment that can be used to show that activity will be sustained for a long time. This yields a self-contained and relatively short proof of existence of a slow phase for arbitrarily large sleep rates.
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