Avalanches in Critical Activated Random Walks

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. Longrange 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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Avalanches in Critical Activated Random Walks

Cited by 3 publications

References 14 publications

Diffusive bounds for the critical density of activated random walks

Diffusive bounds for the critical density of activated random walks

Active Phase for Activated Random Walk on $$\mathbb {Z}$$

Activated Random Walks on $\mathbb{Z}^{d}$

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