Scaling limits in divisible sandpiles: a Fourier multiplier approach

2018/10/15 by Cipriani, Alessandra, de Graaff, Jan, Ruszel, Wioletta M.
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1810.06347

Abstract

In this paper we complete the investigation of scaling limits of the odometer in divisible sandpiles on d-dimensional tori generalising the works Chiarini et al. (2018), Cipriani et al. (2017, 2018). Relaxing the assumption of independence of the weights of the divisible sandpile, we generate generalised 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)^-(1+s) W for s>0 and W a spatial white noise on the d-dimensional unit torus.

Related

• Scaling limit of the odometer in divisible sandpiles
• Constructing fractional Gaussian fields from long-range divisible sandpiles on the torus
• Odometers of Divisible Sandpile Models: Scaling Limits, iDLA and Obstacle Problems. A Survey
• The divisible sandpile with heavy-tailed variables
• Perturbed divisible sandpiles and quadrature surfaces