Scaling Limits in Divisible Sandpiles
| Autor: | Alessandra Cipriani, Wioletta M. Ruszel, Jan van de Graaff |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Pure mathematics Divisible sandpile General Mathematics Gaussian FOS: Physical sciences 01 natural sciences Multiplier (Fourier analysis) 010104 statistics & probability symbols.namesake FOS: Mathematics 0101 mathematics Scaling Mathematical Physics Mathematics Abstract Wiener space Probability (math.PR) 010102 general mathematics Torus Mathematical Physics (math-ph) White noise Fourier analysis Functional Analysis (math.FA) Mathematics - Functional Analysis Fourier transform symbols Generalized Gaussian field Statistics Probability and Uncertainty Mathematics - Probability |
| Zdroj: | Journal of Theoretical Probability, 33 (2020)(4) |
| ISSN: | 0894-9840 |
| Popis: | 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. Comment: 20 pages, 5 figures |
| Databáze: | OpenAIRE |
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