KP governs random growth off a 1-dimensional substrate
The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev–Petviashvili (KP) equation. This is derived algebraically from a Fredholm determinant obtained in [MQR17] for the Kardar–Parisi–Zhang (KPZ)...
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2022-01-01
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| Series: | Forum of Mathematics, Pi |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508621000093/type/journal_article |
| _version_ | 1827994936631361536 |
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| author | Jeremy Quastel Daniel Remenik |
| author_facet | Jeremy Quastel Daniel Remenik |
| author_sort | Jeremy Quastel |
| collection | DOAJ |
| description | The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev–Petviashvili (KP) equation. This is derived algebraically from a Fredholm determinant obtained in [MQR17] for the Kardar–Parisi–Zhang (KPZ) fixed point as the limit of the transition probabilities of TASEP, a special solvable model in the KPZ universality class. The Tracy–Widom distributions appear as special self-similar solutions of the KP and Korteweg–de Vries equations. In addition, it is noted that several known exact solutions of the KPZ equation also solve the KP equation. |
| first_indexed | 2024-04-10T04:48:46Z |
| format | Article |
| id | doaj.art-e06662777a914438bc2dbc546abb9acc |
| institution | Directory Open Access Journal |
| issn | 2050-5086 |
| language | English |
| last_indexed | 2024-04-10T04:48:46Z |
| publishDate | 2022-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Pi |
| spelling | doaj.art-e06662777a914438bc2dbc546abb9acc2023-03-09T12:34:22ZengCambridge University PressForum of Mathematics, Pi2050-50862022-01-011010.1017/fmp.2021.9KP governs random growth off a 1-dimensional substrateJeremy Quastel0Daniel Remenik1Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI-CNRS 2807), Universidad de Chile, Av. Beauchef 851, Torre Norte, Piso 5, Santiago, Chile; E-mail:The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev–Petviashvili (KP) equation. This is derived algebraically from a Fredholm determinant obtained in [MQR17] for the Kardar–Parisi–Zhang (KPZ) fixed point as the limit of the transition probabilities of TASEP, a special solvable model in the KPZ universality class. The Tracy–Widom distributions appear as special self-similar solutions of the KP and Korteweg–de Vries equations. In addition, it is noted that several known exact solutions of the KPZ equation also solve the KP equation.https://www.cambridge.org/core/product/identifier/S2050508621000093/type/journal_article60K3582C22 |
| spellingShingle | Jeremy Quastel Daniel Remenik KP governs random growth off a 1-dimensional substrate Forum of Mathematics, Pi 60K35 82C22 |
| title | KP governs random growth off a 1-dimensional substrate |
| title_full | KP governs random growth off a 1-dimensional substrate |
| title_fullStr | KP governs random growth off a 1-dimensional substrate |
| title_full_unstemmed | KP governs random growth off a 1-dimensional substrate |
| title_short | KP governs random growth off a 1-dimensional substrate |
| title_sort | kp governs random growth off a 1 dimensional substrate |
| topic | 60K35 82C22 |
| url | https://www.cambridge.org/core/product/identifier/S2050508621000093/type/journal_article |
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