Open Access
2020 Activated Random Walks on $\mathbb{Z}^{d}$
Leonardo T. Rolla
Probab. Surveys 17: 478-544 (2020). DOI: 10.1214/19-PS339


Some stochastic systems are particularly interesting as they exhibit critical behavior without fine-tuning of a parameter, a phenomenon called self-organized criticality. In the context of driven-dissipative steady states, one of the main models is that of Activated Random Walks. Long-range effects intrinsic to the conservative dynamics and lack of a simple algebraic structure cause standard tools and techniques to break down. This makes the mathematical study of this model remarkably challenging. Yet, some exciting progress has been made in the last ten years, with the development of a framework of tools and methods which is finally becoming more structured. In these lecture notes we present the existing results and reproduce the techniques developed so far.


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Leonardo T. Rolla. "Activated Random Walks on $\mathbb{Z}^{d}$." Probab. Surveys 17 478 - 544, 2020.


Received: 1 December 2019; Published: 2020
First available in Project Euclid: 23 September 2020

Digital Object Identifier: 10.1214/19-PS339

Primary: 60K35 , 82C22 , 82C26

Keywords: Absorbing-state phase transition

Vol.17 • 2020
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