Duke Mathematical Journal
- Duke Math. J.
- Volume 163, Number 2 (2014), 267-308.
Internal DLA and the Gaussian free field
In previous works, we showed that the internal diffusion-limited aggregation (DLA) cluster on with particles is almost surely spherical up to a maximal error of if and if . This paper addresses average error: in a certain sense, the average deviation of internal DLA from its mean shape is of constant order when and of order (for a radius cluster) in general. Appropriately normalized, the fluctuations (taken over time and space) scale to a variant of the Gaussian free field.
Duke Math. J., Volume 163, Number 2 (2014), 267-308.
First available in Project Euclid: 29 January 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C24: Interface problems; diffusion-limited aggregation
Jerison, David; Levine, Lionel; Sheffield, Scott. Internal DLA and the Gaussian free field. Duke Math. J. 163 (2014), no. 2, 267--308. doi:10.1215/00127094-2430259. https://projecteuclid.org/euclid.dmj/1391007588