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 Probability Surveys > Vol. 17 (2020) open journal systems 


Activated Random Walks on ℤd

Leonardo T. Rolla


Abstract
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.

AMS 2000 subject classifications: Primary 60K35; 82C22; 82C26.

Keywords: Absorbing-state phase transition

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Rolla, Leonardo T., Activated Random Walks on ℤd, Probability Surveys, 17, (2020), 478-544 (electronic). DOI: 10.1214/19-PS339.

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Probability Surveys. ISSN: 1549-5787