Scaling limits of fluctuations of extended-source internal DLA
Abstract In a previous work, we showed that the 2D, extended-source internal DLA (IDLA) of Levine and Peres is δ3/5-close to its scaling limit, if δ is the lattice size. In this paper, we investigate the scaling limits of the fluctuations themselves. Namely, we show that two naturally...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
The Hebrew University Magnes Press
2023
|
| Online Access: | https://hdl.handle.net/1721.1/152341 |
| _version_ | 1826189117039312896 |
|---|---|
| author | Darrow, David |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Darrow, David |
| author_sort | Darrow, David |
| collection | MIT |
| description | Abstract
In a previous work, we showed that the 2D, extended-source internal DLA (IDLA) of Levine and Peres is δ3/5-close to its scaling limit, if δ is the lattice size. In this paper, we investigate the scaling limits of the fluctuations themselves. Namely, we show that two naturally defined error functions, which measure the “lateness” of lattice points at one time and at all times, respectively, converge to geometry-dependent Gaussian random fields. We use these results to calculate point-correlation functions associated with the fluctuations of the flow. Along the way, we demonstrate similar δ3/5 bounds on the fluctuations of the related divisible sandpile model of Levine and Peres, and we generalize the results of our previous work to a larger class of extended sources. |
| first_indexed | 2024-09-23T08:10:07Z |
| format | Article |
| id | mit-1721.1/152341 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:10:07Z |
| publishDate | 2023 |
| publisher | The Hebrew University Magnes Press |
| record_format | dspace |
| spelling | mit-1721.1/1523412024-01-23T18:44:44Z Scaling limits of fluctuations of extended-source internal DLA Darrow, David Massachusetts Institute of Technology. Department of Mathematics Abstract In a previous work, we showed that the 2D, extended-source internal DLA (IDLA) of Levine and Peres is δ3/5-close to its scaling limit, if δ is the lattice size. In this paper, we investigate the scaling limits of the fluctuations themselves. Namely, we show that two naturally defined error functions, which measure the “lateness” of lattice points at one time and at all times, respectively, converge to geometry-dependent Gaussian random fields. We use these results to calculate point-correlation functions associated with the fluctuations of the flow. Along the way, we demonstrate similar δ3/5 bounds on the fluctuations of the related divisible sandpile model of Levine and Peres, and we generalize the results of our previous work to a larger class of extended sources. 2023-10-03T16:00:15Z 2023-10-03T16:00:15Z 2023-06-20 2023-09-24T03:13:46Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/152341 Darrow, David. 2023. "Scaling limits of fluctuations of extended-source internal DLA." en https://doi.org/10.1007/s11854-023-0280-5 Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf The Hebrew University Magnes Press Springer |
| spellingShingle | Darrow, David Scaling limits of fluctuations of extended-source internal DLA |
| title | Scaling limits of fluctuations of extended-source internal DLA |
| title_full | Scaling limits of fluctuations of extended-source internal DLA |
| title_fullStr | Scaling limits of fluctuations of extended-source internal DLA |
| title_full_unstemmed | Scaling limits of fluctuations of extended-source internal DLA |
| title_short | Scaling limits of fluctuations of extended-source internal DLA |
| title_sort | scaling limits of fluctuations of extended source internal dla |
| url | https://hdl.handle.net/1721.1/152341 |
| work_keys_str_mv | AT darrowdavid scalinglimitsoffluctuationsofextendedsourceinternaldla |