Scaling Limits in Divisible Sandpiles: A Fourier Multiplier Approach

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;...

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Bibliographic Details
Published in:Journal of theoretical probability 2020-12, Vol.33 (4), p.2061-2088
Main Authors: Cipriani, Alessandra, de Graaff, Jan, Ruszel, Wioletta M.
Format: Article
Language:English
Subjects:
Covariance
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Scaling
Statistics
Toruses
White noise
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Summary: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 / 2 W for s > 2 and W a spatial white noise on the d -dimensional unit torus.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-019-00952-7