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Pré-Publication, Document De Travail Année : 2023

Jánossy densities and Darboux transformations for the Stark and cylindrical KdV equations

Résumé

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 AmirCorwinQuastel's integro-dierential 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.
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Dates et versions

hal-04049175 , version 1 (28-03-2023)

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  • HAL Id : hal-04049175 , version 1

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Tom Claeys, Gabriel Glesner, Giulio Ruzza, Sofia Tarricone. Jánossy densities and Darboux transformations for the Stark and cylindrical KdV equations. 2023. ⟨hal-04049175⟩
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