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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