Scaling Limits in Divisible Sandpiles

A Fourier Multiplier Approach

Journal Article (2019)
Author(s)

Alessandra Cipriani (TU Delft - Applied Probability)

Jan de Graaff (Student TU Delft)

Wioletta Ruszel (TU Delft - Applied Probability)

Research Group
Applied Probability
Copyright
© 2019 A. Cipriani, Jan de Graaff, W.M. Ruszel
DOI related publication
https://doi.org/10.1007/s10959-019-00952-7
More Info
expand_more
Publication Year
2019
Language
English
Copyright
© 2019 A. Cipriani, Jan de Graaff, W.M. Ruszel
Research Group
Applied Probability
Issue number
4
Volume number
33 (2020)
Pages (from-to)
2061-2088
Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Abstract

In this paper we investigate scaling limits of the odometer in divisible sandpiles on d-dimensional tori following up the works of Chiarini et al. (Odometer of long-range sandpiles in the torus: mean behaviour and scaling limits, 2018), Cipriani et al. (Probab Theory Relat Fields 172:829–868, 2017; Stoch Process Appl 128(9):3054–3081, 2018). Relaxing the assumption of independence of the weights of the divisible sandpile, we generate generalized Gaussian fields in the limit by specifying the Fourier multiplier of their covariance kernel. In particular, using a Fourier multiplier approach, we can recover fractional Gaussian fields of the form (- Δ) - s / 2W for s> 2 and W a spatial white noise on the d-dimensional unit torus.