Moments Match between the KPZ Equation and the Airy Point Process
The results of Amir-Corwin-Quastel,Calabrese-Le Doussal-Rosso,Dotsenko,and Sasamoto-Spohn imply that the one-point distribution of the solution of the KPZ equa-tion with the narrow wedge initial condition coincides with that for a multiplicative statistics of the Airy determinantal random point proc...
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| Format: | Article |
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Raboud University
2018
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| Online Access: | http://hdl.handle.net/1721.1/114025 https://orcid.org/0000-0002-9828-5862 https://orcid.org/0000-0002-2913-5238 |
| _version_ | 1826217360340549632 |
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| author | Borodin, Alexei Gorin, Vadim |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Gorin, Vadim |
| author_sort | Borodin, Alexei |
| collection | MIT |
| description | The results of Amir-Corwin-Quastel,Calabrese-Le Doussal-Rosso,Dotsenko,and Sasamoto-Spohn imply that the one-point distribution of the solution of the KPZ equa-tion with the narrow wedge initial condition coincides with that for a multiplicative statistics of the Airy determinantal random point process. Taking Taylor coefficients of the two sides yields moment identities. We provide a simple direct proof of those via a combinatorial match of their multivariate integral representations. |
| first_indexed | 2024-09-23T17:02:25Z |
| format | Article |
| id | mit-1721.1/114025 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T17:02:25Z |
| publishDate | 2018 |
| publisher | Raboud University |
| record_format | dspace |
| spelling | mit-1721.1/1140252022-10-03T09:58:31Z Moments Match between the KPZ Equation and the Airy Point Process Borodin, Alexei Gorin, Vadim Massachusetts Institute of Technology. Department of Mathematics Gorin, Vadim Borodin, Alexei The results of Amir-Corwin-Quastel,Calabrese-Le Doussal-Rosso,Dotsenko,and Sasamoto-Spohn imply that the one-point distribution of the solution of the KPZ equa-tion with the narrow wedge initial condition coincides with that for a multiplicative statistics of the Airy determinantal random point process. Taking Taylor coefficients of the two sides yields moment identities. We provide a simple direct proof of those via a combinatorial match of their multivariate integral representations. National Science Foundation (U.S.) (Grant DMS-105639) National Science Foundation (U.S.) (Grant DMS-160790) National Science Foundation (U.S.) (Grant DMS-140756) 2018-03-06T14:59:48Z 2018-03-06T14:59:48Z 2016-09 2016-10 2018-03-02T17:43:20Z Article http://purl.org/eprint/type/JournalArticle 1815-0659 http://hdl.handle.net/1721.1/114025 Borodin, Alexei, and Vadim Gorin. “Moments Match Between the KPZ Equation and the Airy Point Process.” Symmetry, Integrability and Geometry: Methods and Applications 12, 102 (October 2016) © 2016 Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Raboud University https://orcid.org/0000-0002-9828-5862 https://orcid.org/0000-0002-2913-5238 http://dx.doi.org/10.3842/SIGMA.2016.102 Symmetry, Integrability and Geometry: Methods and Applications Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) https://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Raboud University Symmetry, Integrability and Geometry: Methods and Applications |
| spellingShingle | Borodin, Alexei Gorin, Vadim Moments Match between the KPZ Equation and the Airy Point Process |
| title | Moments Match between the KPZ Equation and the Airy Point Process |
| title_full | Moments Match between the KPZ Equation and the Airy Point Process |
| title_fullStr | Moments Match between the KPZ Equation and the Airy Point Process |
| title_full_unstemmed | Moments Match between the KPZ Equation and the Airy Point Process |
| title_short | Moments Match between the KPZ Equation and the Airy Point Process |
| title_sort | moments match between the kpz equation and the airy point process |
| url | http://hdl.handle.net/1721.1/114025 https://orcid.org/0000-0002-9828-5862 https://orcid.org/0000-0002-2913-5238 |
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