TY - JOUR
T1 - Scaling Limits in Divisible Sandpiles
T2 - A Fourier Multiplier Approach
AU - Cipriani, Alessandra
AU - de Graaff, Jan
AU - Ruszel, Wioletta M.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Abstract Wiener space
KW - Divisible sandpile
KW - Fourier analysis
KW - Generalized Gaussian field
UR - http://www.scopus.com/inward/record.url?scp=85074951669&partnerID=8YFLogxK
U2 - 10.1007/s10959-019-00952-7
DO - 10.1007/s10959-019-00952-7
M3 - Article
AN - SCOPUS:85074951669
SN - 0894-9840
VL - 33 (2020)
SP - 2061
EP - 2088
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 4
ER -