Dissertations, Theses, and Capstone Projects
Date of Degree
9-2026
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy
Program
Mathematics
Advisor
Matthew Junge
Advisor
Tobias Johnson
Committee Members
Elena Kosygina
Subject Categories
Discrete Mathematics and Combinatorics | Other Mathematics
Abstract
We demonstrate many of the conjectured universality and self-organized criticality (SOC) properties of the interacting particle system Activated Random Walk (ARW) in the setting of one-dimensional biased walks, as formulated for instance in Levine and Silvestri’s 2024 survey. Namely, there exists the same limiting critical state for two finite ARW models, as well as for the infinite model as the density approaches its critical value from below. Many of the desired properties hold, including heavy-tailed avalanches, but spatial correlations decay exponentially fast, a deviation from the SOC paradigm. Nonetheless, the obtained decay rate vanishes with the bias. Since the critical state varies continuously with the bias and has monotonic density, it feasibly converges to the critical state for symmetric ARW. Finally, we prove the conjectured non-fixation behavior at criticality.
Recommended Citation
Meisel, Joshua, "Self-organized criticality in biased activated random walk" (2026). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/6881
