Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions
We construct a family of stochastic growth models in 2 + 1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1 + 1 dimensional growth models in the KPZ class and random tiling models. We show that correlation functions associated to our models have d...
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2016
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| Online Access: | http://hdl.handle.net/1721.1/104915 https://orcid.org/0000-0002-2913-5238 |
| _version_ | 1826194648792563712 |
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| author | Borodin, Alexei Ferrari, Patrik L. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Ferrari, Patrik L. |
| author_sort | Borodin, Alexei |
| collection | MIT |
| description | We construct a family of stochastic growth models in 2 + 1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1 + 1 dimensional growth models in the KPZ class and random tiling models. We show that correlation functions associated to our models have determinantal structure, and we study large time asymptotics for one of the models. The main asymptotic results are: (1) The growing surface has a limit shape that consists of facets interpolated by a curved piece. (2) The one-point fluctuations of the height function in the curved part are asymptotically normal with variance of order ln(t) for time t ≫ 1. (3) There is a map of the (2 + 1)-dimensional space-time to the upper half-plane H such that on space-like submanifolds the multi-point fluctuations of the height function are asymptotically equal to those of the pullback of the Gaussian free (massless) field on H. |
| first_indexed | 2024-09-23T09:59:48Z |
| format | Article |
| id | mit-1721.1/104915 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:59:48Z |
| publishDate | 2016 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1049152022-09-30T18:11:35Z Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions Borodin, Alexei Ferrari, Patrik L. Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei We construct a family of stochastic growth models in 2 + 1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1 + 1 dimensional growth models in the KPZ class and random tiling models. We show that correlation functions associated to our models have determinantal structure, and we study large time asymptotics for one of the models. The main asymptotic results are: (1) The growing surface has a limit shape that consists of facets interpolated by a curved piece. (2) The one-point fluctuations of the height function in the curved part are asymptotically normal with variance of order ln(t) for time t ≫ 1. (3) There is a map of the (2 + 1)-dimensional space-time to the upper half-plane H such that on space-like submanifolds the multi-point fluctuations of the height function are asymptotically equal to those of the pullback of the Gaussian free (massless) field on H. 2016-10-21T18:41:18Z 2016-10-21T18:41:18Z 2013-11 2012-08 2016-08-18T15:24:02Z Article http://purl.org/eprint/type/JournalArticle 0010-3616 1432-0916 http://hdl.handle.net/1721.1/104915 Borodin, Alexei, and Patrik L. Ferrari. “Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions.” Communications in Mathematical Physics 325.2 (2014): 603–684. https://orcid.org/0000-0002-2913-5238 en http://dx.doi.org/10.1007/s00220-013-1823-x Communications in Mathematical Physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer-Verlag Berlin Heidelberg application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Borodin, Alexei Ferrari, Patrik L. Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions |
| title | Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions |
| title_full | Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions |
| title_fullStr | Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions |
| title_full_unstemmed | Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions |
| title_short | Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions |
| title_sort | anisotropic growth of random surfaces in 2 1 dimensions |
| url | http://hdl.handle.net/1721.1/104915 https://orcid.org/0000-0002-2913-5238 |
| work_keys_str_mv | AT borodinalexei anisotropicgrowthofrandomsurfacesin21dimensions AT ferraripatrikl anisotropicgrowthofrandomsurfacesin21dimensions |