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Pré-Publication, Document De Travail Année : 2022

A Riemann Hilbert approach to the study of the generating function associated to Pearcey process

Résumé

Using Riemann-Hilbert problem methods, we establish a Tracy-Widom like formula for generating function of occupancy numbers of the Pearcey process. This formula is linked to a coupled vector differential equation of order 3. We also obtained a non linear coupled heat equation. Combining these two equations leads to a PDE for the logarithm of the Fredholm determinant for the Pearcey process.
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Dates et versions

hal-03770386 , version 1 (06-09-2022)

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  • HAL Id : hal-03770386 , version 1

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Thomas Chouteau. A Riemann Hilbert approach to the study of the generating function associated to Pearcey process. 2022. ⟨hal-03770386⟩
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