Internal DLA and the Gaussian free field
In previous works, we showed that the internal diffusion-limited aggregation (DLA) cluster on Z[superscript d] with t particles is almost surely spherical up to a maximal error of O(logt) if d=2 and O(logt√) if d≥3. This paper addresses average error: in a certain sense, the average deviation of int...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Duke University Press
2015
|
| Online Access: | http://hdl.handle.net/1721.1/92870 https://orcid.org/0000-0002-5951-4933 https://orcid.org/0000-0002-9357-7524 |
| Summary: | In previous works, we showed that the internal diffusion-limited aggregation (DLA) cluster on Z[superscript d] with t particles is almost surely spherical up to a maximal error of O(logt) if d=2 and O(logt√) if d≥3. This paper addresses average error: in a certain sense, the average deviation of internal DLA from its mean shape is of constant order when d=2 and of order r[superscript 1−d/2] (for a radius r cluster) in general. Appropriately normalized, the fluctuations (taken over time and space) scale to a variant of the Gaussian free field. |
|---|