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...
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| Format: | Article |
| Language: | en_US |
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Duke University Press
2015
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| Online Access: | http://hdl.handle.net/1721.1/92870 https://orcid.org/0000-0002-5951-4933 https://orcid.org/0000-0002-9357-7524 |
| _version_ | 1826189544697888768 |
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| author | Jerison, David S. Levine, Lionel Sheffield, Scott Roger |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Jerison, David S. Levine, Lionel Sheffield, Scott Roger |
| author_sort | Jerison, David S. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T08:16:33Z |
| format | Article |
| id | mit-1721.1/92870 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:16:33Z |
| publishDate | 2015 |
| publisher | Duke University Press |
| record_format | dspace |
| spelling | mit-1721.1/928702022-09-23T12:02:12Z Internal DLA and the Gaussian free field Jerison, David S. Levine, Lionel Sheffield, Scott Roger Massachusetts Institute of Technology. Department of Mathematics Jerison, David S. Sheffield, Scott Roger 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. National Science Foundation (U.S.) (grant DMS-0645585) National Science Foundation (U.S.) (grant DMS-1105960) National Science Foundation (U.S.) (Postdoctoral Research Fellowship) National Science Foundation (U.S.) (grant DMS-1069225) 2015-01-14T20:45:14Z 2015-01-14T20:45:14Z 2014-02 2011-03 Article http://purl.org/eprint/type/JournalArticle 0012-7094 1547-7398 http://hdl.handle.net/1721.1/92870 Jerison, David, Lionel Levine, and Scott Sheffield. “Internal DLA and the Gaussian Free Field.” Duke Mathematical Journal 163, no. 2 (February 2014): 267–308. https://orcid.org/0000-0002-5951-4933 https://orcid.org/0000-0002-9357-7524 en_US http://dx.doi.org/10.1215/00127094-2430259 Duke Mathematical Journal Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Duke University Press arXiv |
| spellingShingle | Jerison, David S. Levine, Lionel Sheffield, Scott Roger Internal DLA and the Gaussian free field |
| title | Internal DLA and the Gaussian free field |
| title_full | Internal DLA and the Gaussian free field |
| title_fullStr | Internal DLA and the Gaussian free field |
| title_full_unstemmed | Internal DLA and the Gaussian free field |
| title_short | Internal DLA and the Gaussian free field |
| title_sort | internal dla and the gaussian free field |
| url | http://hdl.handle.net/1721.1/92870 https://orcid.org/0000-0002-5951-4933 https://orcid.org/0000-0002-9357-7524 |
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