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Scaling Limits in Divisible Sandpiles: A Fourier Multiplier Approach
Journal of Theoretical Probability ( IF 0.8 ) Pub Date : 2019-11-07 , DOI: 10.1007/s10959-019-00952-7
Alessandra Cipriani , Jan de Graaff , Wioletta M. Ruszel

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 $(-\Delta)^{-(1+s)} W$ for $s>0$ and $W$ a spatial white noise on the $d$-dimensional unit torus.

中文翻译:

可分沙堆中的标度限制:傅立叶乘法器方法

在本文中,我们完成了对 $d$ 维环面上可分沙堆中里程表缩放限制的研究,概括了 Chiarini 等人的作品。(2018 年),Cipriani 等人。(2017 年,2018 年)。放宽可分沙堆权重独立性的假设,我们通过指定其协方差核的傅立叶乘数来生成极限范围内的广义高斯场。特别是,使用傅立叶乘法器方法,我们可以恢复形式为 $(-\Delta)^{-(1+s)} W$ 的分数高斯场,用于 $s>0$ 和 $W$ 上的空间白噪声$d$ 维单位圆环。
更新日期:2019-11-07
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