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Universality and Sharpness in Activated Random Walks

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Abstract

We consider the activated random walk model in any dimension with any sleep rate and jump distribution and ergodic initial state. We show that the stabilization properties depend only on the average density of particles, regardless of how they are initially located on the lattice.

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Acknowledgements

We thank Ronald Dickman who introduced us to this topic and has been a source of inspiration for almost twenty years. We thank Augusto Teixeira and Lionel Levine for fruitful and encouraging discussions, and Feng Liang who found a gap in an earlier version of the proof. We also thank Roberto Fernández, Krishnamurthi Ravishankar, Frank den Hollander, and Evgene Verbitskiy for valuable help. O.Z. thanks NYU-Shanghai for support and hospitality. O.Z. also thanks support from ANR MALIN. L.R. received support from grants UBACYT-2017 Mod-I 20020160100147BA and PICT 2015-3154.

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Authors and Affiliations

  1. University of Buenos Aires, Buenos Aires, Argentina

    Leonardo T. Rolla

  2. NYU-Shanghai, Shanghai, China

    Leonardo T. Rolla & Vladas Sidoravicius

  3. LPSM (UMR 8001), Sorbonne Université, Paris, France

    Olivier Zindy

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  1. Leonardo T. Rolla
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  2. Vladas Sidoravicius
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  3. Olivier Zindy
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Correspondence to Leonardo T. Rolla.

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Communicated by Anton Bovier.

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Rolla, L.T., Sidoravicius, V. & Zindy, O. Universality and Sharpness in Activated Random Walks. Ann. Henri Poincaré 20, 1823–1835 (2019). https://doi.org/10.1007/s00023-019-00797-0

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