Jánossy densities and Darboux transformations for the Stark and cylindrical KdV equations
arXiv:2303.09848 · doi:10.1007/s00220-024-04988-7
Abstract
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.
arXiv commentV1: 41 pages, 3 figures. V2: 45 pages, 3 figures; revised introduction, minor corrections. V3: 46 pages, 3 figures; minor corrections
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