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The divisible sandpile with heavy-tailed variables

Author

Listed:
  • Cipriani, Alessandra
  • Hazra, Rajat Subhra
  • Ruszel, Wioletta M.

Abstract

This work deals with the divisible sandpile model when an initial configuration sampled from a heavy-tailed distribution. Extending results of Levine et al. (2015) and Cipriani et al. (2016) we determine sufficient conditions for stabilization and non-stabilization on infinite graphs. We determine furthermore that the scaling limit of the odometer on the torus is an α-stable random distribution.

Suggested Citation

  • Cipriani, Alessandra & Hazra, Rajat Subhra & Ruszel, Wioletta M., 2018. "The divisible sandpile with heavy-tailed variables," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3054-3081.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:9:p:3054-3081
    DOI: 10.1016/j.spa.2017.10.013
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    References listed on IDEAS

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    1. Kurt, Noemi, 2007. "Entropic repulsion for a class of Gaussian interface models in high dimensions," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 23-34, January.
    2. Klüppelberg, Claudia & Mikosch, Thomas, 1993. "Spectral estimates and stable processes," Stochastic Processes and their Applications, Elsevier, vol. 47(2), pages 323-344, September.
    3. Dombry, Clément & Jung, Paul, 2014. "A Lindeberg–Feller theorem for stable laws," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 198-203.
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    Cited by:

    1. Alessandra Cipriani & Jan Graaff & Wioletta M. Ruszel, 2020. "Scaling Limits in Divisible Sandpiles: A Fourier Multiplier Approach," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2061-2088, December.

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