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[We consider Activated Random Walks on ℤ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb {Z}$$ \end{document} with totally asymmetric jumps and critical particle density, with different time scales for the progressive release of particles and the dissipation dynamics. We show that the cumulative flow of particles through the origin rescales to a pure-jump self-similar process which we describe explicitly.]
Published: Nov 4, 2020
Keywords: Self-organized criticality; Absorbing-state phase transitions; Avalanches; Scaling limits; Duality; Brownian web; Critical flow; 82C27; 60K35; 82C23; 60K40
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