Transversal Fluctuations of the ASEP, Stochastic Six Vertex Model, and Hall-Littlewood Gibbsian Line Ensembles
Abstract We consider the ASEP and the stochastic six vertex model started with step initial data. After a long time, T, it is known that the one-point height function fluctuations for these systems are of order T1/3. We prove the KPZ prediction of T2/3 scaling in space. Namely, we pro...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/131838 |
| _version_ | 1811076974367473664 |
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| author | Corwin, Ivan Dimitrov, Evgeni |
| author_facet | Corwin, Ivan Dimitrov, Evgeni |
| author_sort | Corwin, Ivan |
| collection | MIT |
| description | Abstract
We consider the ASEP and the stochastic six vertex model started with step initial data. After a long time, T, it is known that the one-point height function fluctuations for these systems are of order T1/3. We prove the KPZ prediction of T2/3 scaling in space. Namely, we prove tightness (and Brownian absolute continuity of all subsequential limits) as T goes to infinity of the height function with spatial coordinate scaled by T2/3 and fluctuations scaled by T1/3. The starting point for proving these results is a connection discovered recently by Borodin–Bufetov–Wheeler between the stochastic six vertex height function and the Hall-Littlewood process (a certain measure on plane partitions). Interpreting this process as a line ensemble with a Gibbsian resampling invariance, we show that the one-point tightness of the top curve can be propagated to the tightness of the entire curve. |
| first_indexed | 2024-09-23T10:33:08Z |
| format | Article |
| id | mit-1721.1/131838 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:33:08Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1318382021-09-21T03:49:16Z Transversal Fluctuations of the ASEP, Stochastic Six Vertex Model, and Hall-Littlewood Gibbsian Line Ensembles Corwin, Ivan Dimitrov, Evgeni Abstract We consider the ASEP and the stochastic six vertex model started with step initial data. After a long time, T, it is known that the one-point height function fluctuations for these systems are of order T1/3. We prove the KPZ prediction of T2/3 scaling in space. Namely, we prove tightness (and Brownian absolute continuity of all subsequential limits) as T goes to infinity of the height function with spatial coordinate scaled by T2/3 and fluctuations scaled by T1/3. The starting point for proving these results is a connection discovered recently by Borodin–Bufetov–Wheeler between the stochastic six vertex height function and the Hall-Littlewood process (a certain measure on plane partitions). Interpreting this process as a line ensemble with a Gibbsian resampling invariance, we show that the one-point tightness of the top curve can be propagated to the tightness of the entire curve. 2021-09-20T17:30:32Z 2021-09-20T17:30:32Z 2018-05-04 2020-09-24T20:49:41Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131838 en https://doi.org/10.1007/s00220-018-3139-3 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Corwin, Ivan Dimitrov, Evgeni Transversal Fluctuations of the ASEP, Stochastic Six Vertex Model, and Hall-Littlewood Gibbsian Line Ensembles |
| title | Transversal Fluctuations of the ASEP, Stochastic Six Vertex Model, and Hall-Littlewood Gibbsian Line Ensembles |
| title_full | Transversal Fluctuations of the ASEP, Stochastic Six Vertex Model, and Hall-Littlewood Gibbsian Line Ensembles |
| title_fullStr | Transversal Fluctuations of the ASEP, Stochastic Six Vertex Model, and Hall-Littlewood Gibbsian Line Ensembles |
| title_full_unstemmed | Transversal Fluctuations of the ASEP, Stochastic Six Vertex Model, and Hall-Littlewood Gibbsian Line Ensembles |
| title_short | Transversal Fluctuations of the ASEP, Stochastic Six Vertex Model, and Hall-Littlewood Gibbsian Line Ensembles |
| title_sort | transversal fluctuations of the asep stochastic six vertex model and hall littlewood gibbsian line ensembles |
| url | https://hdl.handle.net/1721.1/131838 |
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