The divisible sandpile with heavy-tailed variables

Alessandra Cipriani; Rajat Subhra Hazra; Wioletta M. Ruszel

doi:10.1016/j.spa.2017.10.013

The divisible sandpile with heavy-tailed variables

Alessandra Cipriani, Rajat Subhra Hazra, Wioletta M. Ruszel

Applied Probability

Research output: Contribution to journal › Article › Scientific › peer-review

4 Citations (Scopus)

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 -stable random distribution.

Original language	English
Pages (from-to)	3054-3081
Number of pages	28
Journal	Stochastic Processes and their Applications
Volume	128
Issue number	9
DOIs	https://doi.org/10.1016/j.spa.2017.10.013
Publication status	Published - 2018

Keywords

Divisible sandpile
Heavy-tailed variables
α-stable random distribution

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10.1016/j.spa.2017.10.013

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title = "The divisible sandpile with heavy-tailed variables",

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 -stable random distribution.",

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T1 - The divisible sandpile with heavy-tailed variables

AU - Cipriani, Alessandra

AU - Hazra, Rajat Subhra

AU - Ruszel, Wioletta M.

PY - 2018

Y1 - 2018

N2 - 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 -stable random distribution.

AB - 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 -stable random distribution.

KW - Divisible sandpile

KW - Heavy-tailed variables

KW - α-stable random distribution

U2 - 10.1016/j.spa.2017.10.013

DO - 10.1016/j.spa.2017.10.013

M3 - Article

SN - 0304-4149

VL - 128

SP - 3054

EP - 3081

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 9

ER -

The divisible sandpile with heavy-tailed variables

Abstract

Keywords

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