# The transition between the gap probabilities from the Pearcey to the Airy process; a Riemann-Hilbert approach - Mathematical Physics

The transition between the gap probabilities from the Pearcey to the Airy process; a Riemann-Hilbert approach - Mathematical Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: We consider the gap probability for the Pearcey and Airy processes; we set upa Riemann-Hilbert approach different from the standard one whereby theasymptotic analysis for large gap-large time of the Pearcey process is shown tofactorize into two independent Airy processes using the Deift-Zhou steepestdescent analysis. Additionally we relate the theory of Fredholm determinants ofintegrable kernels and the theory of isomonodromic tau function. Using theRiemann-Hilbert problem mentioned above we construct a suitable Lax pairformalism for the Pearcey gap probability and re-derive the two nonlinear PDEsrecently found and additionally find a third one not reducible to those.

Author: ** M. Bertola, M. Cafasso**

Source: https://arxiv.org/