Jánossy densities and Darboux transformations for the Stark and cylindrical KdV equations
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929319759052800 |
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| author | Claeys, Tom Glesner, Gabriel Ruzza, Giulio Tarricone, Sofia |
| author_facet | Claeys, Tom Glesner, Gabriel Ruzza, Giulio Tarricone, Sofia |
| contents | We study Jánossy densities of a randomly thinned Airy kernel determinantal point process. We prove that they can be expressed in terms of solutions to the Stark and cylindrical Korteweg-de Vries equations; these solutions are Darboux tranformations of the simpler ones related to the gap probability of the same thinned Airy point process. Moreover, we prove that the associated wave functions satisfy a variation of Amir-Corwin-Quastel's integro-differential Painlevé II equation. Finally, we derive tail asymptotics for the relevant solutions to the cylindrical Korteweg-de Vries equation and show that they decompose asymptotically into a superposition of simpler solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09848 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Jánossy densities and Darboux transformations for the Stark and cylindrical KdV equations Claeys, Tom Glesner, Gabriel Ruzza, Giulio Tarricone, Sofia Mathematical Physics Probability We study Jánossy densities of a randomly thinned Airy kernel determinantal point process. We prove that they can be expressed in terms of solutions to the Stark and cylindrical Korteweg-de Vries equations; these solutions are Darboux tranformations of the simpler ones related to the gap probability of the same thinned Airy point process. Moreover, we prove that the associated wave functions satisfy a variation of Amir-Corwin-Quastel's integro-differential Painlevé II equation. Finally, we derive tail asymptotics for the relevant solutions to the cylindrical Korteweg-de Vries equation and show that they decompose asymptotically into a superposition of simpler solutions. |
| title | Jánossy densities and Darboux transformations for the Stark and cylindrical KdV equations |
| topic | Mathematical Physics Probability |
| url | https://arxiv.org/abs/2303.09848 |