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 equation with the narrow wedge initial condition coincides with that for a multiplicative statistics of the Airy determinantal random point pr...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148003 |
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| Cite this: | Moments Match between the KPZ Equation and the Airy Point Process / A. Borodin, V. Gorin // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-148003 |
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Borodin, A. Gorin, V. 2019-02-16T16:26:38Z 2019-02-16T16:26:38Z 2016 Moments Match between the KPZ Equation and the Airy Point Process / A. Borodin, V. Gorin // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 60B20; 60H15; 33C10 DOI:10.3842/SIGMA.2016.102 https://nasplib.isofts.kiev.ua/handle/123456789/148003 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 equation 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. This paper is a contribution to the Special Issue on Asymptotics and Universality in Random Matrices, Random Growth Processes, Integrable Systems and Statistical Physics in honor of Percy Deift and Craig Tracy. The full collection is available at http://www.emis.de/journals/SIGMA/Deift-Tracy.html. A.B. was partially supported by the NSF grants DMS-1056390 and DMS-1607901. V.G. was partially supported by the NSF grant DMS-1407562 and by the Sloan Research Fellowship. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Moments Match between the KPZ Equation and the Airy Point Process Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Moments Match between the KPZ Equation and the Airy Point Process |
| spellingShingle |
Moments Match between the KPZ Equation and the Airy Point Process Borodin, A. Gorin, V. |
| title_short |
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_sort |
moments match between the kpz equation and the airy point process |
| author |
Borodin, A. Gorin, V. |
| author_facet |
Borodin, A. Gorin, V. |
| publishDate |
2016 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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 equation 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148003 |
| citation_txt |
Moments Match between the KPZ Equation and the Airy Point Process / A. Borodin, V. Gorin // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 20 назв. — англ. |
| work_keys_str_mv |
AT borodina momentsmatchbetweenthekpzequationandtheairypointprocess AT gorinv momentsmatchbetweenthekpzequationandtheairypointprocess |
| first_indexed |
2025-12-07T20:38:25Z |
| last_indexed |
2025-12-07T20:38:25Z |
| _version_ |
1850883341457293312 |