Abstract
Activated Random Walk is a particle system displaying Self-Organized Criticality, in that the dynamics spontaneously drive the system to a critical state. How universal is this critical state? We state many interlocking conjectures aimed at different aspects of this question: scaling limits, microscopic limits, temporal and spatial mixing, incompressibility, and hyperuniformity.
Acknowledgments
We thank Ahmed Bou-Rabee, Hannah Cairns, Deepak Dhar, Shirshendu Ganguly, Chris Hoffman, Feng Liang, SS Manna, Pradeep Mohanty, Leonardo Rolla, Vladas Sidoravicius, and Lorenzo Taggi for many inspiring conversations. Thanks to Chris Hoffman for pointing out that Conjecture 11 requires a condition on the boundary of , and that Conjecture 17 requires a condition on the driving. We are also grateful to the anonymous referees for carefully reading our article and for many valuable suggestions which improved the presentation. This project was partly supported by the Funds for joint research Cornell-Sapienza. LL was partly supported by the NSF grant DMS-1105960 and IAS Von-Neumann Fellowship. VS was partly supported by Indam-GNAMPA. We thank Cornell University, Sapienza University, IAS, and ICTS-TIFR for their hospitality.
Citation
Lionel Levine. Vittoria Silvestri. "Universality conjectures for activated random walk." Probab. Surveys 21 1 - 27, 2024. https://doi.org/10.1214/24-PS25
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