## Electronic Journal of Probability

### Absorbing-state transition for Stochastic Sandpiles and Activated Random Walks

#### Abstract

We study the dynamics of two conservative lattice gas models on the infinite $d$-dimensional hypercubic lattice: the Activated Random Walks (ARW) and the Stochastic Sandpiles Model (SSM), introduced in the physics literature in the early nineties. Theoretical arguments and numerical analysis predicted that the ARW and SSM undergo a phase transition between an absorbing phase and an active phase as the initial density crosses a critical threshold. However a rigorous proof of the existence of an absorbing phase was known only for one-dimensional systems. In the present work we establish the existence of such phase transition in any dimension. Moreover, we obtain several quantitative bounds for how fast the activity ceases at a given site or on a finite system. The multi-scale analysis developed here can be extended to other contexts providing an efficient tool to study non-equilibrium phase transitions.

#### Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 33, 35 pp.

Dates
Accepted: 15 March 2017
First available in Project Euclid: 13 April 2017

https://projecteuclid.org/euclid.ejp/1492070448

Digital Object Identifier
doi:10.1214/17-EJP50

Mathematical Reviews number (MathSciNet)
MR3646059

Zentralblatt MATH identifier
1362.60089

#### Citation

Sidoravicius, Vladas; Teixeira, Augusto. Absorbing-state transition for Stochastic Sandpiles and Activated Random Walks. Electron. J. Probab. 22 (2017), paper no. 33, 35 pp. doi:10.1214/17-EJP50. https://projecteuclid.org/euclid.ejp/1492070448

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