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Moments Match between the KPZ Equation and the Airy Point Process
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Moments Match between the KPZ Equation and the Airy Point Process
Інший ID:
2010 Mathematics Subject Classification: 60B20; 60H15; 33C10
DOI:10.3842/SIGMA.2016.102
DOI:10.3842/SIGMA.2016.102
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
565
Завантажень:
276
Анотація:
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.
